MATH302 QUIZ 4

Question 1 of 20 0.0/ 1.0 Points

A manufacturer of flashlight batteries took a sample of 13 batteries from a day’s production and used them continuously until they failed to work. The life lengths of the batteries, in hours, until they failed were: 342, 426, 317, 545, 264, 451, 1049, 631, 512, 266, 492, 562, and 298.

At the .05 level of significance, is there evidence to suggest that the mean life length of the batteries produced by this manufacturer is more than 400 hours?

A.No, because the test value 1.257 is greater than the critical value 1.115

B.Yes, because the test value 1.257 is less than the critical value 1.782

C.No, because the p-value for this test is equal to .1164

D.Yes, because the test value 1.257 is less than the critical value 2.179

Question 2 of 20 1.0/ 1.0 Points

Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance.

Compute the z or t value of the sample test statistic.

A.z = 1.96

B.t = 1.645

C.z = 0.69

D.z = 0.62

Question 3 of 20 1.0/ 1.0 Points

Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance.

What is your conclusion?

A.More seniors are going to college

B.Reject H0. There is enough evidence to support the claim that the proportion of students planning to go to college is now greater than .79.

C.Do not reject H0. There is not enough evidence to support the claim that the proportion of students planning to go to college is greater than .79.

D.Cannot determine

Question 4 of 20 1.0/ 1.0 Points

Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance.

State the null and alternative hypotheses.

A.H0: ? = .79, H1: ? > .79

B.H0: p ? .79, H1: p > .79

C.

H0: = .79, H1: > .79

D.H0: p = .79, H1: p ? .79

Question 5 of 20 1.0/ 1.0 Points

A two-tailed test is one where:

A.negative sample means lead to rejection of the null hypothesis

B.results in either of two directions can lead to rejection of the null hypothesis

C.no results lead to the rejection of the null hypothesis

D.results in only one direction can lead to rejection of the null hypothesis

Question 6 of 20 1.0/ 1.0 Points

The “Pizza Hot” manager commits a Type I error if he/she is

A.staying with old style when new style is no better than old style

B.switching to new style when it is no better than old style

C.switching to new style when it is better than old style

D.staying with old style when new style is better

Question 7 of 20 1.0/ 1.0 Points

The hypothesis that an analyst is trying to prove is called the:

A.elective hypothesis

B.quality of the researcher

C.level of significance

D.alternative hypothesis

Question 8 of 20 1.0/ 1.0 Points

A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy is a variance in measurements of 1.2 or less. If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2, does this provide enough evidence to reject the claim that the lab technician’s accuracy is within the target accuracy?

Compute the value of the appropriate test statistic.

A. = 27.50

B. = 30.58

C.t = 27.50

D.z = 1.65

Question 9 of 20 0.0/ 1.0 Points

You conduct a hypothesis test and you observe values for the sample mean and sample standard deviation when n = 25 that do not lead to the rejection of H0. You calculate a p-value of 0.0667. What will happen to the p-value if you observe the same sample mean and standard deviation for a sample size larger than 25?

A.The p – value may increase or decrease

B.The p – value decreases

C.The p – value increases

D.The p – value stays the same

Question 10 of 20 1.0/ 1.0 Points

A type I error occurs when the:

A.sample mean differs from the population mean

B.null hypothesis is incorrectly rejected when it is true

C.null hypothesis is incorrectly accepted when it is false

D.test is biased

Question 11 of 20 1.0/ 1.0 Points

If a teacher is trying to prove that a new method of teaching economics is more effective than a traditional one, he/she will conduct a:

A.one-tailed test

B.point estimate of the population parameter

C.confidence interval

D.two-tailed test

Part 2 of 3 - 6.0/ 6.0 Points

Question 12 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.

The ABC battery company claims that their batteries last at least 100 hours, on average. Your experience with their batteries has been somewhat different, so you decide to conduct a test to see if the company's claim is true. You believe that the mean life is actually less than the 100 hours the company claims. You decide to collect data on the average battery life (in hours) of a random sample of n = 20 batteries. Some of the information related to the hypothesis test is presented below.

Test of H0: 100 versus H1: 100

Sample mean 98.5

Std error of mean 0.777

Assuming the life length of batteries is normally distributed, if you wish to conduct this test using a .05 level of significance, what is the critical value that you should use? Place your answer, rounded to 3 decimal places in the blank. For example, -1.234 would be a legitimate entry. -1.729

Question 13 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.

Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with = 2.8%. A random sample of 16 Australian bank stocks has a sample mean dividend yield of 8.91%. For the entire Australian stock market, the mean dividend yield is = 6.4%. If you wanted to test, at a .05 level of significance, to determine if these data indicate that the dividend yield of all Australian bank stocks is higher than 6.4% what is the critical value that you would use? Place your answer, rounded to 2 decimal places, in the blank. For example, 2.345 would be a legitimate entry. 1.65

Question 14 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.

The CEO of a software company is committed to expanding the proportion of highly qualified women in the organization’s staff of salespersons. He believes that the proportion of women in similar sales positions across the country is less than 45%. Hoping to find support for his belief, he directs you to test

H0: p .45 vs H1: p < .45.

In doing so, you collect a random sample of 50 salespersons employed by his company, which is thought to be representative of sales staffs of competing organizations in the industry. The collected random sample of size 50 showed that only 18 were women.

Compute the p-value associated with this test. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry. 0.1004

Question 15 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.

At a university, the average cost of books per student has been $400 per student per semester. The Dean of Students believes that the costs are increasing and that the average is now greater than $400. He surveys a sample of 40 students and finds that for the most recent semester their average cost was $430 with a standard deviation of $80. What is the test value for this hypothesis test?

Question 16 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.

The CEO of a software company is committed to expanding the proportion of highly qualified women in the organization’s staff of salespersons. He believes that the proportion of women in similar sales positions across the country is less than 45%. Hoping to find support for his belief, he directs you to test

H0: p .45 vs H1: p < .45.

In doing so, you collect a random sample of 50 salespersons employed by his company, which is thought to be representative of sales staffs of competing organizations in the industry. The collected random sample of size 50 showed that only 18 were women.

Compute the test value that you would use in conducting this test. Place your answer, rounded to 3 decimal places, in the blank. For example, -2.345 would be a legitimate entry. -1.279

Question 17 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 firm that produces light bulbs claims that their lightbulbs last 1500 hours, on average. You wonder if the average might differ from the 1500 hours that the firm claims. To explore this possibility you take a random sample of n = 25 light bulbs purchased from this firm and record the lifetime (in hours) of each bulb. You then conduct an appopriate test of hypothesis. Some of the information related to the hypothesis test is presented below.

Test of H0: = 1500 versus H1: 1500

Sample mean 1509.5

Std error of mean 4.854

Assuming the life length of this type of lightbulb is normally distributed, what is the p-value associated with this test? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.234 would be a legitimate entry. 0.062

Part 3 of 3 - 3.0/ 3.0 Points

Question 18 of 20 1.0/ 1.0 Points

In order to determine the p-value, it is unnecessary to know the level of significance.

True

False

Question 19 of 20 1.0/ 1.0 Points

Using the confidence interval when conducting a two-tailed test for the population proportion p, we reject the null hypothesis if the hypothesized value for p falls inside the confidence interval.

True

False

Question 20 of 20 1.0/ 1.0 Points

A one-tailed alternative is one that is supported by evidence in either direction.

True

False