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# apu math 302 quiz 3

Question # 00006053
Subject: Statistics
Due on: 01/31/2014
Posted On: 01/03/2014 12:00 AM

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Question 1 of 20

0.0/ 1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of 12 employees reveals the following family dental expenses (in dollars): 115, 370, 250, 593, 540, 225, 177, 425, 318, 182, 275, and 228.

Construct a 99% confidence interval estimate for the standard deviation of family dental expenses for all employees of this corporation.

Place your LOWER limit, in dollars rounded to 1 decimal place, in the first blank. Do not use a dollar sign, a comma, or any other stray mark. For example, 98.4 would be a legitimate entry. Correct175.5

Place your UPPER limit, in dollars rounded to 1 decimal place, in the second blank. Do not use a dollar sign, a comma, or any other stray mark. For example, 567.8 would be a legitimate entry. Correct440.8

Question 2 of 20

0.0/ 1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Senior management of a consulting services firm is concerned about a growing decline in the firm’s weekly number of billable hours. The firm expects each professional employee to spend at least 40 hours per week on work. In an effort to understand this problem better, management would like to estimate the standard deviation of the number of hours their employees spend on work-related activities in a typical week. Rather than reviewing the records of all the firm’s full-time employees, the management randomly selected a sample of size 51 from the available frame. The sample mean and sample standard deviations were 48.5 and 7.5 hours, respectively.

Construct a 90% confidence interval for the standard deviation of the number of hours this firm’s employees spend on work-related activities in a typical week.

Place your LOWER limit, in hours, rounded to 1 decimal place, in the first blank. For example, 6.7 would be a legitimate entry. Correct46.8

Place your UPPER limit, in hours, rounded to 1 decimal place, in the second blank. For example, 12.3 would be a legitimate entry. Correct50.2

Question 3 of 20

0.0/ 1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound-shaped and symmetric with a mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28?

Answer: Correct.1037 Round your answer to 4 decimal places as necessary. For example, 0.1357 would be a legitimate entry.

Feedback: This is a sampling distribution problem with ? = 25.9. ? = 9.5, and sample size n = 30.

f[z=frac{28-25.9}{9.5/sqrt{30}} = 1.210755f]

P(z > 1.210755) = 1 – NORMSDIST(1.210755) = 0.1130

Or you can compute the probability without having to compute z first:

P(x-bar > 28) = 1 – NORMDIST(28, 25.9, 9.5/SQRT(30), TRUE) = 0.1130

Question 4 of 20

1.0/ 1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

You are told that a random sample of 150 people from Iowa has been given cholesterol tests, and 60 of these people had levels over the “safe” count of 200. Construct a 95% confidence interval for the population proportion of people in Iowa with cholesterol levels over 200. Place your LOWER limit, rounded to 3 decimal places, in the first blank Correct.322 . For example, .678 would be a legitimate entry. Place your UPPER limit, rounded to 3 decimal places, in the second blank Correct.478 . For example, .789 would be a legitimate entry.

Question 5 of 20

1.0/ 1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Senior management of a consulting services firm is concerned about a growing decline in the firm’s weekly number of billable hours. The firm expects each professional employee to spend at least 40 hours per week on work. In an effort to understand this problem better, management would like to estimate the standard deviation of the number of hours their employees spend on work-related activities in a typical week. Rather than reviewing the records of all the firm’s full-time employees, the management randomly selected a sample of size 51 from the available frame. The sample mean and sample standard deviations were 48.5 and 7.5 hours, respectively.

Construct a 95% confidence interval for the standard deviation of the number of hours this firm’s employees spend on work-related activities in a typical week.

Place your LOWER limit, in hours, rounded to 1 decimal place, in the first blank. For example, 6.7 would be a legitimate entry. Correct6.3

Place your UPPER limit, in hours, rounded to 1 decimal place, in the second blank. For example, 12.3 would be a legitimate entry. Correct9.3

Question 6 of 20

1.0/ 1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A marketing research consultant hired by Coca-Cola is interested in determining the proportion of customers who favor Coke over other soft drinks. A random sample of 400 consumers was selected from the market under investigation and showed that 53% favored Coca-Cola over other brands.

Compute a 95% confidence interval for the true proportion of people who favor Coke. Place your LOWER limit, rounded to 3 decimal places, in the first blank Correct.481 . For example, .345 would be a legitimate entry. Place your UPPER limit in the second blank Correct.579 . For example, .456 would be a legitimate entry.

Question 7 of 20

0.0/ 1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of 12 employees reveals the following family dental expenses (in dollars): 115, 370, 250, 593, 540, 225, 177, 425, 318, 182, 275, and 228.

Construct a 90% confidence interval estimate for the standard deviation of family dental expenses for all employees of this corporation.

Place your LOWER limit, in dollars rounded to 1 decimal place, in the first blank. Do not use a dollar sign, a comma, or any other stray mark. For example, 123.4 would be a legitimate entry. Correct231.5

Place your UPPER limit, in dollars rounded to 1 decimal place, in the second blank. Do not use a dollar sign, a comma, or any other stray mark. For example, 567.8 would be a legitimate entry. Correct384.9

Part 2 of 3 - 10.0/ 11.0 Points

Question 8 of 20

1.0/ 1.0 Points

In constructing a confidence interval estimate for a population mean, when we replace f\$sigma f\$ with the sample standard deviation (s), we introduce a new source of variability and the sampling distribution we use is:

A.F- distribution

B.the normal distribution

C.chi-square distribution

Correct D.t -distribution

Question 9 of 20

1.0/ 1.0 Points

A food snack manufacturer samples 15 bags of pretzels off the assembly line and weighed their contents. If the sample mean is 10.0 and the sample standard deviation is 0.15, find the 95% confidence interval estimate for the true mean.

A.(9.96, 10.04)

B.(9.68, 10.32)

C.(9.97, 10.80)

Correct D.(9.92, 10.08)

Question 10 of 20

1.0/ 1.0 Points

In a study of elephants a researcher wishes to determine the average weight of a certain subspecies of elephants. From previous studies, the standard deviation of the weights of elephants in this subspecies is known to be 1500 pounds. How many elephants does the researcher need to weigh so that he can be 80% confident that the average weight of elephants in his sample is within 350 pounds of the true average weight for this subspecies?

A.50

B.39

C.166

Correct

Question 11 of 20

0.0/ 1.0 Points

If you increase the confidence level, the confidence interval ____________.

A.stays the same

B.decreases

C.increases

Incorrect D.may increase or decrease, depending on the sample data

Question 12 of 20

1.0/ 1.0 Points

The average gas mileage of a certain model car is 26 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 1.3, find the probability that a randomly selected car of this model has a gas mileage between 25.8 and 26.3 miles per gallon.

Correct A.0.15

B.0.85

C.0.70

D.0.30

Question 13 of 20

1.0/ 1.0 Points

At a large department store, the average number of years of employment for a cashier is 5.7 with a standard deviation of 1.8 years. If the number of years of employment at this department store is normally distributed, what is the probability that a cashier selected at random has worked at the store for over 10 years?

A.0.4916

B.0.9916

Correct C.0.0084

D.0.0054

Question 14 of 20

1.0/ 1.0 Points

In order to be accepted into a top university, applicants must score within the top 5% on the SAT exam. Given that SAT test scores are normally distributed with a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university?

Correct A.1330

B.1400

C.1250

D.1100

Question 15 of 20

1.0/ 1.0 Points

From a sample of 500 items, 30 were found to be defective. The point estimate of the population proportion defective will be:

A.30

B.0.60

C.16.667

Correct D..06

Question 16 of 20

1.0/ 1.0 Points

The upper limit of the 90% confidence interval for the population proportion p, given that n = 100; and f\$hat{p}f\$ = 0.20 is

A.0.4684

Correct B.0.2658

C.0.5316

D.0.7342

Question 17 of 20

1.0/ 1.0 Points

Which of the following will make a confidence interval narrower and more precise?

A.Larger sample size and higher confidence level

B.Smaller sample size and lower confidence level

Correct C.Larger sample size and lower confidence level

D.Smaller sample size and higher confidence level

Question 18 of 20

1.0/ 1.0 Points

The t- distribution for developing a confidence interval for a mean has _____ degrees of freedom.

A.n - 2

B.n + 1

Correct C.n - 1

D.n

Part 3 of 3 - 2.0/ 2.0 Points

Question 19 of 20

1.0/ 1.0 Points

The lower limit of the 95% confidence interval for the population proportion p, given that n = 300; and f\$hat{p}f\$ = 0.10 is 0.1339.

Correct

True

False

Question 20 of 20

1.0/ 1.0 Points

The upper limit of the 90% confidence interval for the population proportion p, given that n = 100; and f\$hat{p}f\$ = 0.20 is 0.2341.

Correct

True

False

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#### apu math 302 quiz 3

Tutorial # 00005823
Posted On: 01/03/2014 12:01 AM
Posted By:
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10154
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Tutorial Preview …in xxx form xx + bi) xxxxx "a" and xxx need xx xxxx explicitly xxxxxx values For xxxxxxxx {1+1i} is xxxxx whereas xxxxx xx not xxxxxx is valid xxxxxxx {9i} is xxx Senior xxxxxxxxxx xx a xxxxxxxxxx services firm xx concerned about x growing xxxxxxx xx the xxxxxxxx weekly number xx billable hours xxx firm xxxxxxx xxxx professional xxxxxxxx to spend xx least 40 xxxxx per xxxx xx work xx an effort xx understand this xxxxxxx better, xxxxxxxxxx xxxxx like xx estimate the xxxxxxxx deviation of xxx number xx xxxxx their xxxxxxxxx spend on xxxxxxxxxxxx activities in x typical xxxx xxxxxx than xxxxxxxxx the records xx all the xxxxxxxx full-time xxxxxxxxxx xxx management xxxxxxxx selected a xxxxxx of size xx from xxx xxxxxxxxx frame xxx sample mean xxx sample standard xxxxxxxxxx were xx x and x 5 hours, xxxxxxxxxxxx Construct a xxx confidence xxxxxxxx xxx the xxxxxxxx deviation of xxx number of xxxxx this xxxxxxxx xxxxxxxxx spend xx work-related activities xx a typical xxxx Place xxxx xxxxx limit, xx hours, rounded xx 1 decimal xxxxxx in xxx xxxxx blank xxx example, 6 x would be x legitimate xxxxx xxxxxxxx 3 xxxxx your UPPER xxxxxx in hours, xxxxxxx to x xxxxxxx place, xx the second xxxxx For example, xx 3 xxxxx xx a xxxxxxxxxx entry Correct9 x Answer Key: xxxxxxxx 6 xx xx 1 xx 1 0 xxxxxx Accepted characters: xxxxxxxx decimal xxxxx xxxxxxx (period xx comma), sign xxxxxxxxxx (-), spaces xx g x xx thousands xxxxxxxxxx 5 000), xxx or "e" xxxxx in xxxxxxxxxx xxxxxxxxx NOTE: xxx scientific notation, x period MUST xx used xx xxx decimal xxxxx marker Complex xxxxxxx should be xx the xxxx xx + xxx where "a" xxx "b" need xx have xxxxxxxxxx xxxxxx values xxx example: {1+1i} xx valid whereas xxxxx is xxx xxxxxx is xxxxx whereas {9i} xx not A xxxxxxxxx research xxxxxxxxxx xxxxx by xxxxxxxxx is interested xx determining the xxxxxxxxxx of xxxxxxxxx xxx favor xxxx over other xxxx drinks A xxxxxx sample xx xxx consumers xxx selected from xxx market under xxxxxxxxxxxxx and xxxxxx xxxx 53% xxxxxxx Coca-Cola over xxxxx brands Compute x 95% xxxxxxxxxx xxxxxxxx for xxx true proportion xx people who xxxxx Coke xxxxx xxxx LOWER xxxxxx rounded to x decimal places, xx the xxxxx xxxxx Correct xxx For example, xxx would be x legitimate xxxxx xxxxx your xxxxx limit in xxx second blank xxxxxxx 579 xxx xxxxxxxx 456 xxxxx be a xxxxxxxxxx entry Answer xxxx Question x xx 20 x 0/ 1 x Points Accepted xxxxxxxxxxx numbers, xxxxxxx xxxxx markers xxxxxxx or comma), xxxx indicators (-), xxxxxx (e x x as xxxxxxxxx separator, 5 xxxxx "E" or xxx (used xx xxxxxxxxxx notation) xxxxx For scientific xxxxxxxxx a period xxxx be xxxx xx the xxxxxxx point marker xxxxxxx numbers should xx in xxx xxxx (a…
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Preview: its xxxxxxxxx to xxxxxxxxx the feasibility xx providing a xxxxxx insurance xxxx x random xxxxxx of 12 xxxxxxxxx reveals the xxxxxxxxx family xxxxxx xxxxxxxx (in xxxxxxxxx 115, 370, xxxx 593, 540, xxxx 177, xxxx xxxx 182, xxxx and 228 xxxxxxxxxxx a 99% xxxxxxxxxx interval xxxxxxxx xxx the xxxxxxxx deviation of xxxxxx dental expenses xxx all xxxxxxxxx xx this xxxxxxxxxxx  Place your xxxxx limit, in xxxxxxx rounded xx x decimal xxxxxx in the xxxxx blank Do xxx use x xxxxxx sign, x comma, or xxx other stray xxxx For xxxxxxxx xx 4 xxxxx be a xxxxxxxxxx entry  175 xxxxxxxx your xxxxx xxxxxx in xxxxxxx rounded to x decimal place, xx the xxxxxx xxxxx Do xxx use a xxxxxx sign, a xxxxxx or xxx xxxxx stray xxxx For example, xxx 8 would xx a xxxxxxxxxx xxxxx  440 xxxxxxxxx Key: 94 7|94 xx 304 0|304 xxxxxxxxx 2 xx xxx 0/ x 0 PointsAccepted xxxxxxxxxxx numbers, decimal xxxxx markers xxxxxxx xx comma), xxxx indicators (-), xxxxxx (e g x as xxxxxxxxx xxxxxxxxxx 5 xxxxx "E" or xxx (used in xxxxxxxxxx notation) xxxxxxxxxxxx xxxxxxxxxx notation, x period MUST xx used as xxx decimal xxxxx xxxxxx  Complex xxxxxxx should be xx the form xx + xxx xxxxx "a" xxx "b" need xx have explicitly xxxxxx values xxxxx xxxxxxxx {1+1i} xx valid whereas xxxxx is not xxxxxx is xxxxx xxxxxxx {9i} xx not  Senior xxxxxxxxxx of a xxxxxxxxxx services xxxx xx concerned xxxxx a growing xxxxxxx in the xxxxxxxx weekly xxxxxx xx billable xxxxx The firm xxxxxxx each professional xxxxxxxx to xxxxx xx least xx hours per xxxx on work xx an xxxxxx xx understand xxxx problem better, xxxxxxxxxx would like xx estimate xxx xxxxxxxx deviation xx the number xx hours their xxxxxxxxx spend xx xxxxxxxxxxxx activities xx a typical xxxx Rather than xxxxxxxxx the xxxxxxx xx all xxx firm’s full-time xxxxxxxxxx the management xxxxxxxx selected x xxxxxx of xxxx 51 from xxx available frame xxx sample xxxx xxx sample xxxxxxxx deviations were xx 5 and x 5 xxxxxx xxxxxxxxxxxx  Construct x 90% confidence xxxxxxxx for the xxxxxxxx deviation xx xxx number xx hours this xxxxxxxx employees spend xx work-related xxxxxxxxxx xx a xxxxxxx week  Place xxxx LOWER limit, xx hours, xxxxxxx xx 1 xxxxxxx place, in xxx first blank xxx example, x x would xx a legitimate xxxxx  46 8 Place xxxx UPPER xxxxxx xx hours, xxxxxxx to 1 xxxxxxx place, in xxx second xxxxx xxx example, xx 3 would xx a legitimate xxxxx  50 xxxxxxxxx xxxxxxx 4|6 xx 8 9|9 xxxxxxxxx 3 of xxx 0/ x x PointsAccepted xxxxxxxxxxx numbers, decimal xxxxx markers (period xx comma), xxxx xxxxxxxxxx (-), xxxxxx (e g x as thousands xxxxxxxxxx 5 xxxxx xxx or xxx (used.....
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