MAT2058 all week homeworks latest 2018 july

Question # 00708891 Posted By: rey_writer Updated on: 08/01/2018 06:05 AM Due on: 08/01/2018
Subject Mathematics Topic General Mathematics Tutorials:
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Week 1 homework

Question 1 . A polling company reported that 57?% of 1013 surveyed adults said that secondhand smoke is "very harmful." Complete parts? (a) through? (d) below.

a. What is the exact value that is 57?% of 1013??

b. Could the result from part? (a) be the actual number of adults who said that secondhand smoke is "very harmful" question mark Why or why? not?

A.

?No, the result from part? (a) could not be the actual number of adults who said that secondhand smoke is "very harmful" because a count of people must result in a whole number.

B.

?No, the result from part? (a) could not be the actual number of adults who said that secondhand smoke is "very harmful" because that is a very rare opinion.

C.

?Yes, the result from part? (a) could be the actual number of adults who said that secondhand smoke is "very harmful" because the polling numbers are accurate.

D.

?Yes, the result from part? (a) could be the actual number of adults who said that secondhand smoke is "very harmful" because the results are statistically significant.

c. What could be the actual number of adults who said that secondhand smoke is "very harmful" ?

The actual number of adults with this opinion could be

d. Among the 1013 ?respondents, 110 said that secondhand smoke is "not at all harmful." What percentage of respondents said that secondhand smoke is "not at all harmful" ?

Question2 Determine whether the given value is a statistic or a parameter.

A survey found that 91 % of all respondents were optimistic.

Choose the correct answer below.

A.

The value is a statistic because it is a numerical measurement describing some characteristic of a population.

B.

The value is a parameter because it is a numerical measurement describing some characteristic of a population.

C.

The value is a parameter because it is a numerical measurement describing some characteristic of a sample.

D.

The value is a statistic because it is a numerical measurement describing some characteristic of a sample.

Question 3 . Identify the level of measurement of the? data, and explain what is wrong with the given calculation.

In a set of? data, mood levels are represented as 100 for bad comma 200 for OK comma and 300 for good. The average? (mean) of the 682 mood levels is 231.2 .

The data are at the level of measurement.

What is wrong with the given? calculation?

A.

The true average is 195.4.

B.

Such data should not be used for calculations such as an average.

C.

One must use a different method to take the average of such data.

D.

There is nothing wrong with the given calculation.

Question 4 Identify the type of sampling used? (random, systematic,? convenience, stratified, or cluster? sampling) in the situation described below.

A woman is selected by a marketing company to participate in a paid focus group. The company says that the woman was selected because everyone in five randomly selected towns was being selected. nothing nothing

Which type of sampling did the marketing company? use?

Cluster sampling

Systematic sampling

Stratified sampling

Random sampling

Convenience sampling

Question 5 Determine whether the sample described below is a simple random sample.

According to an insurance salesman?, names of potential customers are selected from a variety of different sources. Names from the list are randomly selected in a way that is equivalent to writing the names on slips of? paper, mixing them in a? bowl, and selecting the required number of potential customers.

Does this sampling plan result in a simple random? sample?

A.

The sample is a simple random sample because each individual has the same chance of being selected.

B.

The sample is not a simple random sample because each individual does not have the same chance of being selected.

C.

The sample is not a simple random sample because every sample of the same size does not have the same chance of being selected.

D.

The sample is a simple random sample because every sample of the same size has the same chance of being selected.

Question 6 Listed below are the top 10 annual salaries? (in millions of? dollars) of TV personalities. Find the? (a) mean,? (b) median,? (c) mode, and? (d) midrange for the given sample data in millions of dollars. Given that these are the top 10? salaries, do we know anything about the salaries of TV personalities in? general? Are such top 10 lists valuable for gaining insight into the larger? population?

38.2???36.8???35.1???26.5???15.9???13.2???11.9???10.8???9.9???8.1

a. The mean is

?(Type an integer or a? decimal.)

b. The median is

?(Type an integer or a? decimal.)

c. Select the correct choice below and fill in any answer boxes in your choice.

A.

The mode is

nothing.

?(Use a comma to separate answers as? needed.)

B.

There is no mode.

d. The midrange is

?(Type an integer or a? decimal.)

Given that these are the top 10? salaries, do we know anything about the salaries of TV personalities in? general?

A.

Since the? mean, median, and midrange are relatively reliable even with small? samples, a lot of information is given on the salaries of TV personalities in general.

B.

Since the sample values give information about one segment of the salaries of TV? personalities, they give a lot of information about the salaries of TV personalities in general.

C.

Since the sample values are the 10? highest, they give almost no information about the salaries of TV personalities in general.

D.

Since the? mean, median, and midrange are based on a small? sample, no information is given on the salaries of TV personalities in general.

Are such top 10 lists valuable for gaining insight into the larger? population?

A.

?No, because such top 10 lists represent an extreme subset of the population rather than the larger population

B.

?Yes, because the? mean, median, and midrange are relatively reliable even with small samples

C.

?No, because the? mean, median, and midrange are based on a small sample

D.

?Yes, because such top 10 lists give partial information about the population

Question 7 Listed below are the errors between the predicted temperatures and actual temperatures of a certain city. Find the mean and median for each of the two samples. Do the means and medians indicate that the temperatures predicted one day in advance are more accurate than those predicted 5 days in? advance, as we might? expect?

left parenthesis actual high right parenthesis minus left parenthesis predicted high 1 day earlier right parenthesis

1

1

1

negative 1

negative 3

2

1

negative 1

1

2

left parenthesis actual high right parenthesis minus left parenthesis predicted high 5 days earlier right parenthesis

5

0

negative 1

0

0

0

0

0

negative 2

negative 5

The mean difference between actual high and the predicted high one day earlier is

?(Type an integer or decimal rounded to the nearest tenth as? needed.)

The median difference between actual high and the predicted high one day earlier is

?(Type an integer or decimal rounded to the nearest tenth as? needed.)

The mean difference between actual high and the predicted high five days earlier is

?(Type an integer or decimal rounded to the nearest tenth as? needed.)

The median difference between actual high and the predicted high five days earlier is

?(Type an integer or decimal rounded to the nearest tenth as? needed.)

Do the means and medians indicate that the temperatures predicted one day in advance are more accurate than those predicted 5 days in? advance, as we might? expect?

A.

?No, the means and medians do not indicate any substantial difference in accuracy.

B.

?No, the means and medians indicate that predictions made five days in advance are more accurate.

C.

?Yes, the means and medians indicate that predictions made one day in advance are more accurate.

Question 8 Listed below are the durations? (in hours) of a simple random sample of all flights of a space shuttle program. Find the? range, variance, and standard deviation for the sample data. Is the lowest duration time? unusual? Why or why? not?

74???98???235???194???166???260???200???376???260???234???383???331???220???246???0

The range of the sample data is

The variance of the sample data is

?(Round to one decimal place as? needed.)

The standard deviation of the sample data is

?(Round to one decimal place as? needed.)

Is the lowest duration time unusual?? Why or why? not?

A.

?No, because it is within two standard deviations of the mean.

B.

?Yes, because the lowest value in a data set is usually an outlier.

C.

?No, because the sample is random.

D.

?Yes, because it is more than two standard deviations below the mean.

Question 9 One of the tallest living men has a height of 272 cm. One of the tallest living women is 264 cm tall. Heights of men have a mean of 175 cm and a standard deviation of 9 cm. Heights of women have a mean of 165 cm and a standard deviation of 6 cm. Relative to the population of the same? gender, who is? taller? Explain.

Choose the correct answer below.

A.

The woman is relatively taller because the z score for her height is less than the z score for the man?'s height.

B.

The woman is relatively taller because the z score for her height is greater than the z score for the man?'s height

C.

The man is relatively taller because the z score for his height is greater than the z score for the woman?'s height.

D.

The man is relatively taller because the z score for his height is less than the z score for the woman?'s height.

Question 10. Below are 36 sorted ages of an acting award winner. Find the percentile corresponding to age 60 using the method presented in the textbook.

16

17

17

18

18

19

19

23

24

24

26

28

28

32

38

39

40

40

45

46

49

56

56

59

60

62

63

63

68

71

72

72

74

76

76

77

percentile of value 60 = ?(Round to the nearest integer as? needed.)

Homework 2

1. Heights of men on a baseball team have a? bell-shaped distribution with a mean of 183 cm and a standard deviation of 7 cm. Using the empirical? rule, what is the approximate percentage of the men between the following? values?

a. 162 cm and 204 cm

b. 176 cm and 190 cm

a. _________of the men are between 162 cm and 204 cm.

?(Round to one decimal place as? needed.)

b. _____of the men are between 176 cm and 190 cm.

?(Round to one decimal place as? needed.)

2. Cans of regular soda have volumes with a mean of 12.72 oz and a standard deviation of 0.11 oz. Is it unusual for a can to contain 13.1 oz of? soda?

Minimum? "usual"

?(Type an integer or a? decimal.)

Maximum? "usual

?(Type an integer or a? decimal.)

Is 13.1 oz an? "unusual" volume?

A.

Yes comma because it is larger than the maximum "usual" value.

.B.

?Yes, because it is smaller than the minimum? "usual" value.

C.

?No, because it is smaller than the minimum? "usual" value.

D.

No comma because it is between the minimum and maximum "usual" values.

E.

?Yes, because it is between the minimum and maximum? "usual" values.

F.

?No, because it is larger than the maximum? "usual" value.

3.Five males with a particular genetic disorder have one child each. The random variable x is the number of children among the five who inherit the genetic disorder. Determine whether the table describes a probability distribution. If it? does, find the mean and standard deviation.

x

0

1

2

3

4

5

?P(x)

0.00210.0021

0.02510.0251

0.12290.1229

0.30100.3010

0.36850.3685

0.1804

Find the mean of the random variable x. Select the correct choice below? and, if? necessary, fill in the answer box to complete your choice.

A.

muequals

B.

The table is not a probability distribution.

Find the standard deviation of the random variable x. Select the correct choice below? and, if? necessary, fill in the answer box to complete your choice.

A.

sigmaequals

1.0 ?(Round to one decimal place as? needed.)

B.

The table is not a probability distribution.

4. Heights of women have a? bell-shaped distribution with a mean of 156 cm and a standard deviation of 8 cm. Using? Chebyshev's theorem, what do we know about the percentage of women with heights that are within 3 standard deviations of the? mean? What are the minimum and maximum heights that are within 3 standard deviations of the? mean?

At least ______ of women have heights within 3 standard deviations of 156 cm.

?(Round to the nearest percent as? needed.)

The minimum height that is within 3 standard deviations of the mean is _________cm.

The maximum height that is within 3 standard deviations of the mean is ________cm.

5. The accompanying table describes results from eight offspring peas. The random variable x represents the number of offspring peas with green pods. Complete parts? (a) through? (d).

Probabilities of Numbers of Peas with Green Pods Among 8 Offspring Peas

x (Number of Peas with Green Pods)

P(x)

0

0+

1

0+

2

0.0030.003

3

0.0290.029

4

0.0840.084

5

0.1740.174

6

0.3620.362

7

0.2570.257

8

0.0910.091

a. Find the probability of getting exactly 7 peas with green pods.

b. Find the probability of getting 7 or more peas with green pods.

c. Which probability is relevant for determining whether 7 is an unusually high number of peas with green? pods, the result from part? (a) or part? (b)?

The result from part? (a)

The result from part? (b)

d. Is 7 an unusually high number of peas with green? pods? Why or why? not? Use 0.05 as the threshold for an unusual event.

A.

?No, since the appropriate probability is greater than? 0.05, it is not an unusually high number.

B.

?No, since the appropriate probability is less than? 0.05, it is not an unusually high number.

C.

?Yes, since the appropriate probability is less than? 0.05, it is an unusually high number.

D.

?Yes, since the appropriate probability is greater than? 0.05, it is an unusually high number.

6. Determine whether the given procedure results in a binomial distribution. If it is not? binomial, identify the requirements that are not satisfied.

Recording the genders of 50 people in a statistics class nothing

Choose the correct answer below.

A.

No comma because there are more than two possible outcomes.

B.

Yes comma because all 4 requirements are satisfied.

C.

?No, because the probability of success does not remain the same in all trials.

D.

?No, because there are more than two possible outcomes and the trials are not independent.

7. Fifteen peas are generated from parents having the? green/yellow pair of? genes, so there is a 0.75 probability that an individual pea will have a green pod. Find the probability that among the 15 offspring? peas, no more than 1 has a green pod. Is it unusual to get no more than 1 pea with a green pod when 15 offspring peas are? generated? Why or why? not?

The probability that no more than 1 of the 15 offspring peas has a green pod is ___

?(Round to three decimal places as? needed.)

Is it unusual to randomly select 15 peas and find that no more than 1 of them have a green? pod? Note that a small probability is one that is less than 0.05.

A.

Yes?, because the probability of this occurring is very small.

B.

No?, because the probability of this occurring is very small.

C.

No?, because the probability of this occurring is not small.

D.

Yes?, because the probability of this occurring is not small.

8. A brand name has a 50?% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 5 randomly selected consumers. Complete parts? (a) through? (d) below.

a. What is the probability that exactly 4 of the selected consumers recognize the brand? name?

The probability that exactly 4 of the 5 consumers recognize the brand name is _______?(Round to three decimal places as? needed.)

b. What is the probability that all of the selected consumers recognize the brand? name?

The probability that all of the selected consumers recognize the brand name is ________?(Round to three decimal places as? needed.)

c. What is the probability that at least 4 of the selected consumers recognize the brand? name?

The probability that at least 4 of the selected consumers recognize the brand name is ____?(Round to three decimal places as? needed.)

d. If 5 consumers are randomly? selected, is 4 an unusually high number of consumers that recognize the brand? name?

A.

Yes?, because the probability that 4 or more of the selected consumers recognize the brand name is greater than 0.05.

B.

No?, because the probability that 4 or more of the selected consumers recognize the brand name is greater than 0.05.

C.

Yes?, because the probability that 4 or more of the selected consumers recognize the brand name is less than 0.05.

D.

No?, because the probability that 4 or more of the selected consumers recognize the brand name is less than 0.05.

9. Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean mu and standard deviation sigma. ?Also, use the range rule of thumb to find the minimum usual value mu minus 2 sigma and the maximum usual value mu plus 2 sigma.

nequals1450?, pequals3/5

mu=

sigma=

mu minus 2 sigma=

mu plus 2 sigma =

10. a. For classes of 166 ?students, find the mean and standard deviation for the number born on the 4th of July. Ignore leap years.

b. For a class of 166 ?students, would two be an unusually high number who were born on the 4th of? July?

a. The value of the mean is mu=

?(Round to six decimal places as? needed.)

The value of the standard deviation is sigma=

b. Would 2 be an unusually high number of individuals who were born on the 4th of? July?

A.

No comma because 2 is within the range of usual values.

B.

Yes comma because 2 is greater than the maximum usual value.

C.

Yes comma because 2 is below the minimum usual value.

D.

This result is unlikely because 2 is within the range of usual values.

Homework 3

1. Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

Click to view page 1 of the table. LOADING... Click to view page 2 of the table. LOADING...

2. Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

3. Find the area of the shaded region. The graph to the right depicts IQ scores of? adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

4. Find the area of the shaded region. The graph to the right depicts IQ scores of? adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

5. Find the indicated IQ score. The graph to the right depicts IQ scores of? adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

6. A survey found that? women's heights are normally distributed with mean 62.6 in. and standard deviation 2.3 in. The survey also found that? men's heights are normally distributed with a mean 68.3 in. and standard deviation 2.8. Complete parts a through c below.

a. Most of the live characters at an amusement park have height requirements with a minimum of 4 ft 9 in. and a maximum of 6 ft 3 in. Find the percentage of women meeting the height requirement.

The percentage of women who meet the height requirement is _____?(Round to two decimal places as? needed.)

b. Find the percentage of men meeting the height requirement.

The percentage of men who meet the height requirement is ______?(Round to two decimal places as? needed.)

c. If the height requirements are changed to exclude only the tallest? 5% of men and the shortest? 5% of? women, what are the new height? requirements?

The new height requirements are at least _____and at most ______?(Round to one decimal place as? needed.)

7. Which of the following is NOT a property of the sampling distribution of the sample? mean?

Choose the correct answer below.

A.

The distribution of the sample mean tends to be skewed to the right or left.

B.

The mean of the sample means is the population mean.

C.

The sample means target the value of the population mean.

D.

The expected value of the sample mean is equal to the population mean.

8. Assume that? women's heights are normally distributed with a mean given by mu equals 64.1 in?, and a standard deviation given by sigma equals 2.6 in.

?(a) If 1 woman is randomly? selected, find the probability that her height is less than 65 in.

?(b) If 31 women are randomly? selected, find the probability that they have a mean height less than 65 in.

?(?a) The probability is approximately ?(Round to four decimal places as? needed.)

?(b) The probability is approximately ?(Round to four decimal places as? needed.

9. An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 211 lb. The new population of pilots has normally distributed weights with a mean of 158 lb and a standard deviation of 31.2 lb.

a. If a pilot is randomly? selected, find the probability that his weight is between 150 lb and 211 lb.

The probability is approximately _________?(Round to four decimal places as? needed.)

b. If 33 different pilots are randomly? selected, find the probability that their mean weight is between 150 lb and 211 lb.

The probability is approximately _______?(Round to four decimal places as? needed.)

c. When redesigning the ejection? seat, which probability is more? relevant?

A.

Part? (b) because the seat performance for a single pilot is more important.

B.

Part? (a) because the seat performance for a sample of pilots is more important.

C.

Part? (b) because the seat performance for a sample of pilots is more important.

D.

Part? (a) because the seat performance for a single pilot is more important.

10. If np greater than or equals 5 and nq greater than or equals 5?, estimate Upper P left parenthesis fewer than 6 right parenthesis with nequals13 and pequals0.6 by using the normal distribution as an approximation to the binomial? distribution; if npless than5 or nqless than?5, then state that the normal approximation is not suitable.

Select the correct choice below? and, if? necessary, fill in the answer box to complete your choice.

A.

Upper P left parenthesis fewer than 6 right parenthesis = ___?(Round to four decimal places as? needed.)

.B.

The normal approximation is not suitable

Homework 4

1. A newspaper provided a? "snapshot" illustrating poll results from 1910 professionals who interview job applicants. The illustration showed that? 26% of them said the biggest interview turnoff is that the applicant did not make an effort to learn about the job or the company. The margin of error was given as plus or minus 3 percentage points. What important feature of the poll was? omitted?

Choose the correct answer.

The point estimate

The confidence level

The sample size

The confidence interval

2. Find the critical value z Subscript alpha divided by 2 that corresponds to the given confidence level.

96?%

z Subscript alpha divided by 2equals

3. In a poll of 598 human resource? professionals, 46.3?% said that body piercings and tattoos were big grooming red flags. Complete parts? (a) through? (d) below.

?a) Among the 598 human resource professionals who were? surveyed, how many of them said that body piercings and tattoos were big grooming red? flags?

________?(Round to the nearest integer as? needed.)

?b) Construct a? 99% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big grooming red flags.

_______ less than p less than ____________?(Round to three decimal places as? needed.)

?c) Repeat part? (b) using a confidence level of? 80%.______less than p less than______?(Round to three decimal places as? needed.)

?d) Compare the confidence intervals from parts? (b) and? (c) and identify the interval that is wider. Why is it? wider?

Select the correct choice below and fill in the answer boxes to complete your choice.

A.

The

nothing?% confidence interval is wider than the

nothing?% confidence interval. As the confidence interval? narrows, the probability that the confidence interval actually does contain the sample parameter increases.

B.

The

nothing?% confidence interval is wider than the

nothing?% confidence interval. As the confidence interval? widens, the probability that the confidence interval actually does contain the sample parameter increases.

C.

The

nothing?% confidence interval is wider than the

nothing?% confidence interval. As the confidence interval? narrows, the probability that the confidence interval actually does contain the population parameter increases.

D.

The ____confidence interval is wider than the ______confidence interval. As the confidence interval? widens, the probability that the confidence interval actually does contain the population parameter increases.

4. Do one of the? following, as appropriate.? (a) Find the critical value z Subscript alpha divided by 2?, ?(b) find the critical value t Subscript alpha divided by 2?, ?(c) state that neither the normal nor the t distribution applies.

Confidence level 95?%; nequals20?; sigma is known?; population appears to be very skewed.

Find the critical value.

A.

t Subscript alpha divided by 2 Baseline equals 2.093

B.

z Subscript alpha divided by 2equals1.645

C.

z Subscript alpha divided by 2 Baseline equals 1.96

D.

t Subscript alpha divided by 2equals1.729

E.

Neither normal nor t distribution applies.

5. In a test of the effectiveness of garlic for lowering? cholesterol, 44 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol? (in mg/dL) have a mean of 3.5 and a standard deviation of 17.1. Complete parts? (a) and? (b) below.

a. What is the best point estimate of the population mean net change in LDL cholesterol after the garlic? treatment?

The best point estimate is _______?mg/dL.

?(Type an integer or a? decimal.)

b. Construct a 95?% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL? cholesterol?

What is the confidence interval estimate of the population mean mu??

?(Round to two decimal places as? needed.)

What does the confidence interval suggest about the effectiveness of the? treatment?

A.

The confidence interval limits contain ?0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.

B.

The confidence interval limits do not contain ?0, suggesting that the garlic treatment did affect the LDL cholesterol levels.

C.

The confidence interval limits contain ?0, suggesting that the garlic treatment did affect the LDL cholesterol levels.

D.

The confidence interval limits do not contain ?0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.

6. Twelve different video games showing substance use were observed and the duration times of game play? (in seconds) are listed below. The design of the study justifies the assumption that the sample can be treated as a simple random sample. Use the data to construct a 95?% confidence interval estimate of mu?, the mean duration of game play.

4045

3886

3854

4023

4313

4820

4654

4039

5000

4831

4335

4324

What is the confidence interval estimate of the population mean mu??

?(Round to one decimal place as? needed.)

7. An IQ test is designed so that the mean is 100 and the standard deviation is 16 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99?% confidence that the sample mean is within 4 IQ points of the true mean. Assume that sigmaequals16 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

The required sample size is _____?(Round up to the nearest? integer.)

Would it be reasonable to sample this number of? students?

No. This number of IQ test scores is a fairly large number.

Yes. This number of IQ test scores is a fairly large number.

No. This number of IQ test scores is a fairly small number.

Yes. This number of IQ test scores is a fairly small number.

8. If we find that there is a linear correlation between the concentration of carbon dioxide in our atmosphere and the global? temperature, does that indicate that changes in the concentration of carbon dioxide cause changes in the global? temperature?

Choose the correct answer below.

A.

Yes. The presence of a linear correlation between two variables implies that one of the variables is the cause of the other variable.

B.

No. The presence of a linear correlation between two variables does not imply that one of the variables is the cause of the other variable.

9. For a sample of eight? bears, researchers measured the distances around the? bears' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is requals0.989. Using alpha = 0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest? size?

a. Is there a linear correlation between chest size and? weight?

A.

?No, because the absolute value of the test statistic exceeds the critical value of 0.707.

B.

?Yes, because the test statistic falls between the critical values of negative 0.707 and 0.707.

C.

?Yes, because the absolute value of the test statistic exceeds the critical value of 0.707.

D.

The answer cannot be determined from the given information.

b. What proportion of the variation in weight can be explained by the linear relationship between weight and chest? size?

?(Round to three decimal places as? needed.)

10. Listed below are amounts of court income and salaries paid to the town justices. All amounts are in thousands of dollars. Construct a? scatterplot, find the value of the linear correlation coefficient? r, and find the? P-value using alphaequals0.05. Is there sufficient evidence to conclude that there is a linear correlation between court incomes and justice? salaries? Based on the? results, does it appear that justices might profit by levying larger? fines?

Court Income

65.0

406.0

1567.0

1131.0

272.0

251.0

111.0

155.0

31.0

Justice Salary

31

44

94

58

46

62

26

27

19

What are the null and alternative? hypotheses?

A.

Upper H 0?: rhoequals0

Upper H 1?: rhonot equals0

.B.

Upper H 0?: rhoequals0

Upper H 1?: rhogreater than0

C.

Upper H 0?: rhoequals0

Upper H 1?: rholess than0

D.

Upper H 0?: rhonot equals0

Upper H 1?: rhoequals0

Construct a scatterplot. Choose the correct graph below.

A.

0

800

1600

0

50

100

Court Income

Justice Salary

A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (220, 84); (220, 80); (360, 80); (400, 70); (580, 84); (740, 58); (1080, 62); (1120, 30); (1420, 44).

B.

0

800

1600

0

50

100

Court Income

Justice Salary

A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (140, 14); (140, 36); (340, 42); (660, 54); (740, 66); (900, 74); (1280, 90); (1320, 14); (1420, 74).

C.

0

800

1600

0

50

100

Court Income

Justice Salary

A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (40, 20); (60, 32); (120, 26); (160, 28); (260, 62); (280, 46); (400, 44); (1140, 58); (1560, 94).

D.

0

800

1600

0

50

100

Court Income

Justice Salary

A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (260, 84); (420, 24); (640, 56); (760, 86); (880, 48); (900, 34); (1040, 86); (1260, 46); (1480, 18).

The linear correlation coefficient r is _____?(Round to three decimal places as? needed.)

The test statistic t is ______?(Round to three decimal places as? needed.)

The? P-value is ____?(Round to three decimal places as? needed.)

Because the? P-value is ____than the significance level 0.05?, there _____sufficient evidence to support the claim that there is a linear correlation between court incomes and justice salaries for a significance level of alphaequals0.05.

Based on the? results, does it appear that justices might profit by levying larger? fines?

A.

It appears that justices profit the same despite the amount of the fines.

B.

It does appear that justices might profit by issuing smaller fines.

C.

It does not appear that justices might profit by levying larger fines.

D.

It does appear that justices might profit by levying larger fines.

Homework 5

1. The claim is that the proportion of peas with yellow pods is equal to 0.25? (or 25%). The sample statistics from one experiment include 400 peas with 115 of them having yellow pods. Find the value of the test statistic.

The value of the test statistic is ____-?(Round to two decimal places as? needed.)

2. Assume that the significance level is alpha equals 0.01. Use the given information to find the? P-value and the critical? value(s).

The test statistic of zequals1.78 is obtained when testing the claim that p greater than 0.4.

Click here to view page 1 of the Normal table. LOADING... Click here to view page 2 of the Normal table. LOADING...

?P-value = _____-?(Round to four decimal places as? needed.)

The critical? value(s) is/are z = _____?(Round to two decimal places as needed. Use a comma to separate answers as? needed.)

3. Assume a significance level of alpha equals 0.05 and use the given information to complete parts? (a) and? (b) below.

Original? claim: The proportion of male golfers is more than 0.8. The hypothesis test results in a? P-value of 0.007.

a. State a conclusion about the null hypothesis.? (Reject Upper H 0 or fail to reject Upper H 0?.) Choose the correct answer below.

A.

Reject Upper H 0 because the? P-value is greater than alpha.

B.

Reject Upper H 0 because the? P-value is less than alpha.

C.

Fail to reject Upper H 0 because the? P-value is greater than alpha.

D.

Fail to reject Upper H 0 because the? P-value is less than alpha.

b. Without using technical? terms, state a final conclusion that addresses the original claim. Which of the following is the correct? conclusion?

A.

There is not sufficient evidence to reject the claim that the proportion of male golfers is??more than 0.8.

B.

There is sufficient evidence to reject the claim that the proportion of male golfers is??more than 0.8.

C.

There is sufficient evidence to support the claim that the proportion of male golfers is more than 0.8.

D.

There is not sufficient evidence to support the claim that the proportion of male golfers is more than 0.8.

4. Identify the type I error and the type II error that correspond to the given hypothesis.

The percentage of adults who retire at age 65 is less than 62 %.

Identify the type I error. Choose the correct answer below.

A.

Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is less than 62 % when the percentage is actually equal to 62 %.

B.

Reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62 % when that percentage is actually equal to 62 %.

C.

Reject the null hypothesis that the percentage of adults who retire at age 65 is less than 62 % when that percentage is actually less than 62 %.

D.

Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62 % when that percentage is actually less than 62 %.

Identify the type II error. Choose the correct answer below.

A.

Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62 % when that percentage is actually less than 62 %.

B.

Reject the null hypothesis that the percentage of adults who retire at age 65 is less than 62 % when that percentage is actually less than 62 %.

C.

Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is less than 62 % when the percentage is actually equal to 62 %.

D.

Reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62 % when the percentage is actually equal to 62 %.

5. A genetic experiment involving peas yielded one sample of offspring consisting of 430 green peas and 156 yellow peas. Use a 0.05 significance level to test the claim that under the same? circumstances, 26?% of offspring peas will be yellow. Identify the null? hypothesis, alternative? hypothesis, test? statistic, P-value, conclusion about the null? hypothesis, and final conclusion that addresses the original claim. Use the? P-value method and the normal distribution as an approximation to the binomial distribution.

What are the null and alternative? hypotheses?

A.

Upper H 0 : p not equals 0.26

Upper H 1 : p equals 0.26

B.

Upper H 0 : p not equals 0.26

Upper H 1 : p greater than 0.26

C.

Upper H 0 : p equals 0.26

Upper H 1 : p greater than 0.26

D.

Upper H 0 : p equals 0.26

Upper H 1 : p less than 0.26

E.

Upper H 0 : p not equals 0.26

Upper H 1 : p less than 0.26

F.

Upper H 0 : p equals 0.26

Upper H 1 : p not equals 0.26.

What is the test? statistic?

Z = _________?(Round to two decimal places as? needed.)

What is the? P-value?

?P-value =__________?(Round to four decimal places as? needed.)

What is the conclusion about the null? hypothesis?

A.

Reject the null hypothesis because the? P-value is less than or equal to the significance? level, alpha.

B.

Fail to reject the null hypothesis because the? P-value is greater than the significance? level, alpha.

C.

Reject the null hypothesis because the? P-value is greater than the significance? level, alpha.

D.

Fail to reject the null hypothesis because the? P-value is less than or equal to the significance? level, alpha.

What is the final? conclusion?

A.

There is sufficient evidence to support the claim that less than 26?% of offspring peas will be yellow.

B.

There is sufficient evidence to warrant rejection of the claim that 26?% of offspring peas will be yellow.

C.

There is not sufficient evidence to support the claim that less than 26?% of offspring peas will be yellow.

D.

There is not sufficient evidence to warrant rejection of the claim that 26?% of offspring peas will be yellow.

6. Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative? hypotheses, test? statistic, P-value, and state the final conclusion that addresses the original claim.

A simple random sample of 25 filtered 100 mm cigarettes is? obtained, and the tar content of each cigarette is measured. The sample has a mean of 19.0 mg and a standard deviation of 3.54 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 ?mg, which is the mean for unfiltered king size cigarettes. What do the results? suggest, if? anything, about the effectiveness of the? filters?

What are the? hypotheses?

A.

Upper H 0?: muless than21.1 mg

Upper H 1?: mugreater than or equals21.1 mg

B.

Upper H 0?: muequals21.1 mg

Upper H 1?: mugreater than or equals21.1 mg

C.

Upper H 0?: mugreater than21.1 mg

Upper H 1?: muless than21.1 mg

D.

Upper H 0?: muequals21.1 mg

Upper H 1?: muless than21.1 mg

Identify the test statistic.

T = _______?(Round to three decimal places as? needed.)

Identify the? P-value.

The? P-value is ______?(Round to four decimal places as? needed.)

State the final conclusion that addresses the original claim. Choose the correct answer below.

A.

Reject Upper H 0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

B.

Fail to reject Upper H 0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

C.

Reject Upper H 0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

D.

Fail to reject Upper H 0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

What do the results? suggest, if? anything, about the effectiveness of the? filters?

A.

The results suggest that the filters increase the tar content.

B.

The results are inconclusive because the sample size is less than 30.

C.

The results suggest that the filtered cigarettes have the same tar content as unfiltered king size cigarettes.

D.

The results suggest that the filters are effective.

E.

The results do not suggest that the filters are effective.

7. The accompanying data table lists measured voltage amounts supplied directly to a? family's home. The power supply company states that it has a target power supply of 120 volts. Using those home voltage? amounts, test the claim that the mean is 120 volts. Use a 0.05 significance level.

Day

Volts

1

124.5124.5

2

123.9123.9

3

123.9123.9

4

123.7123.7

5

123.4123.4

6

123.3123.3

7

123.3123.3

8

123.6123.6

9

123.5123.5

10

123.9123.9

11

123.5123.5

12

123.7123.7

13

124.3124.3

14

123.7123.7

15

123.9123.9

16

124.0124.0

17

124.2124.2

18

124.1124.1

19

123.8123.8

20

123.8123.8

Day

Volts

21

124.0124.0

22

123.9123.9

23

123.6123.6

24

123.8123.8

25

123.4123.4

26

123.4123.4

27

123.4123.4

28

123.4123.4

29

123.3123.3

30

123.9123.9

31

123.5123.5

32

123.6123.6

33

123.6123.6

34

123.9123.9

35

123.9123.9

36

123.8123.8

37

123.9123.9

38

123.7123.7

39

123.8123.8

40

123.8

What are the null and alternative? hypotheses?

A.

Upper H 0?: muequals120

Upper H 1?: mugreater than120

B.

Upper H 0?: muequals120

Upper H 1?: munot equals120

.C.

Upper H 0?: munot equals120

Upper H 1?: muequals120

D.

Upper H 0?: munot equals120

Upper H 1?: mugreater than120

Calculate the test statistic.

?(Round to three decimal places as? needed.)

What is the range of values for the? P-value?

Choose the correct answer below.

A.

Upper P dash value less than 0.01

B.

0.10 less than Upper P dash value less than 0.20

C.

0.025 less than Upper P dash value less than 0.05

D.

Upper P dash value greater than 0.20

E.

0.01 less than Upper P dash value less than 0.025

F.

0.05 less than Upper P dash value less than 0.10

Identify the critical? value(s).

?(Round to three decimal places as needed. Use a comma to separate answers as? needed.)

State the final conclusion that addresses the original claim.______Upper H 0. There is _____evidence to warrant rejection of the claim that the mean voltage is 120 volts.

8. What is the difference between the following two regression? equations?

ModifyingAbove y with caret equals b 0 plus b 1 x y equals beta 0 plus beta 1 x

Choose the correct answer below.

A.

The first equation is for a? population; the second equation is for sample data.

B.

The first equation is for sample? data; the second equation is for a population.

9. Suppose IQ scores were obtained from randomly selected twins. For 20 such pairs of? people, the linear correlation coefficient is 0.948 and the equation of the regression line is ModifyingAbove y with caret equals negative 13.53 plus 1.12 x?, where x represents the IQ score of the twin born second. ?Also, the 20 x values have a mean of 101.82 and the 20 y values have a mean of 100.05. What is the best predicted IQ of the twin born first?, given that the twin born second has an IQ of 110?? Use a significance level of 0.05.

Critical Values of the Pearson Correlation Coefficient r

?NOTE: To test

H0?:

rho?equals=0

against

H1?:

rho?not equals??0,

reject

H0

if the absolute value of r is greater than the critical value in the table.

n

alpha?equals=0.05

alpha?equals=0.01

4

0.950

0.990

5

0.878

0.959

6

0.811

0.917

7

0.754

0.875

8

0.707

0.834

9

0.666

0.798

10

0.632

0.765

11

0.602

0.735

12

0.576

0.708

13

0.553

0.684

14

0.532

0.661

15

0.514

0.641

16

0.497

0.623

17

0.482

0.606

18

0.468

0.590

19

0.456

0.575

20

0.444

0.561

25

0.396

0.505

30

0.361

0.463

35

0.335

0.430

40

0.312

0.402

45

0.294

0.378

50

0.279

0.361

60

0.254

0.330

70

0.236

0.305

80

0.220

0.286

90

0.207

0.269

100

0.196

0.256

n

alpha?equals=0.05

alpha?equals=0.01

The best predicted IQ of the twin born first is_____.

?(Round to two decimal places as? needed.)

10. The data show the time intervals after an eruption? (to the next? eruption) of a certain geyser. Find the regression? equation, letting the first variable be the independent? (x) variable. Find the best predicted time of the interval after an eruption given that the current eruption has a height of 127 feet. Use a significance level of 0.05.

Height? (ft)

70

73

104

122

74

107

76

97

Interval after? (min)

69

62

82

91

71

84

68

75

What is the regression? equation?

? (Round to two decimal places as? needed.)

What is the best predicted time for the interval after an eruption that is 127 feet? high?

The best predicted interval time for an eruption that is 127 feet high is ____?(Round to one decimal place as? needed.)

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