AnswersCA-Statistics and Probability BIntroduction to Hypothesis Testing

Preparing to Test a Claim about a Population Proportion Answers

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1
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It is believed that 80% of adults are honest. An honesty experiment was conducted on a random sample of 50 adults. It was discovered that 42 of the adults were honest. The researcher would like to know if the data provide convincing evidence that more than 80% of adults are honest. What are the values of the test statistic and P-value for this test?Find the z-table here.

A
z = StartStartFraction 0.84 minus 0.8 OverOver StartRoot StartFraction 0.8 (1 minus 0.8) Over 50 EndFraction EndEndFraction, p-value = 0.4778
Option A
B
z = StartStartFraction 0.84 minus 0.8 OverOver StartRoot StartFraction 0.8 (1 minus 0.8) Over 50 EndFraction EndEndFraction, p-value = 0.2389
Option B
C
z = StartStartFraction 0.8 minus 0.84 OverOver StartRoot StartFraction 0.84 (1 minus 0.84) Over 50 EndFraction EndEndFraction, p-value = 0.2389
Option C
D
z = StartStartFraction 0.8 minus 0.84 OverOver StartRoot StartFraction 0.84 (1 minus 0.84) Over 50 EndFraction EndEndFraction, p-value = 0.4778
Option D
2
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It is believed that 80% of adults are honest. An honesty experiment was conducted on a random sample of 50 adults. It was discovered that 42 of the adults were honest. The researcher would like to know if the data provide convincing evidence that more than 80% of adults are honest. The standardized test statistic is z = 0.71 and the P-value is 0.2389. What conclusion should be made using the = 0.10 significance level?

Question illustration
A
Because the P-value is greater than = 0.10, there is convincing evidence that more than 80% of adults are honest.
Option A
B
Because the P-value is greater than = 0.10, there is not convincing evidence that more than 80% of adults are honest.
Option B
C
Because the test statistic is greater than = 0.10, there is convincing evidence that more than 80% of adults are honest.
Option C
D
Because the test statistic is greater than = 0.10, there is not convincing evidence that more than 80% of adults are honest.
Option D
3

According to historical data, it is believed that 12% of American adults work more than one job. To investigate if this claim is still accurate today, a random sample of 100 American adults is selected. It is discovered that 18 of them work more than one job. A researcher would like to know if the data provide convincing evidence that the true proportion of American adults who work more than one job differs from 12%. The standardized test statistic is z = 1.85 and the P-value is 0.0644. What decision should the researcher make using the = 0.05 significance level?

Question illustration
A
Reject H0 because the P-value is greater than = 0.05.
Option A
B
Reject Ha because the P-value is greater than = 0.05.
Option B
C
Fail to reject H0 because the P-value is greater than = 0.05.
Option C
D
Fail to reject Ha because the P-value is greater than = 0.05.
Option D
4

It is claimed that 95% of teenagers who have a cell phone never leave home without it. To investigate this claim, a random sample of 300 teenagers who have a cell phone was selected. It was discovered that 273 of the teenagers in the sample never leave home without their cell phone. One question of interest is whether the data provide convincing evidence that the true proportion of teenagers who never leave home without a cell phone is less than 95%. What are the values of the test statistic and P-value for this test?Find the z-table here.

A
z = 3.18, P-value = 0.0007
B
z = –3.18, P-value = 0.0007
C
z = 3.18, P-value = 0.0014
D
z = –3.18, P-value = 0.0014
5

A teacher claims that 55% of her statistics students have a strong understanding of inference for one proportion. To investigate this claim she randomly selects 25 of her 50 statistics students and provides them with an inference problem about one proportion. Of the 25 selected students, 14 demonstrate a strong understanding of inference for one proportion. The teacher would like to know if the data provide convincing evidence that more than 55% of her students have a strong understanding of this topic. Are the conditions for inference met?

A
Yes, the conditions for inference are met.
B
No, the 10% condition is not met.
C
No, the Large Counts Condition is not met.
D
No, the randomness condition is not met.
6

A reporter claims that 90% of American adults cannot name the current vice president of the United States. To investigate this claim, the reporter selects a random sample of 50 American adults and finds that 28 are unable to name the current vice president. The reporter would like to know if the data provide convincing evidence that fewer than 90% of American adults are unable to name the current vice president. Are the conditions for inference met?

A
Yes, the conditions for inference are met.
B
No, the 10% condition is not met.
C
No, the Large Counts Condition is not met.
D
No, the randomness condition is not met.
7

A nutritionist believes that 10% of teenagers eat cereal for breakfast. To investigate this claim, she selects a random sample of 150 teenagers and finds that 25 eat cereal for breakfast. She would like to know if the data provide convincing evidence that the true proportion of teenagers who eat cereal for breakfast differs from 10%. The standardized test statistic is z = 2.72 and the P-value is 0.0066. What conclusion should be made using the = 0.05 significance level?

Question illustration
A
Because the P-value is less than = 0.05, there is convincing evidence that the true proportion of teenagers who eat cereal for breakfast is 10%.
Option A
B
Because the P-value is less than = 0.05, there is not convincing evidence that the true proportion of teenagers who eat cereal for breakfast is 10%.
Option B
C
Because the P-value is less than = 0.05, there is convincing evidence that the true proportion of teenagers who eat cereal for breakfast differs from 10%.
Option C
D
Because the P-value is less than = 0.05, there is not convincing evidence that the true proportion of teenagers who eat cereal for breakfast differs from 10%.
Option D
8

A nutritionist believes that 10% of teenagers eat cereal for breakfast. To investigate this claim, she selects a random sample of 150 teenagers and finds that 25 eat cereal for breakfast. She would like to know if the data provide convincing evidence that the true proportion of teenagers who eat cereal for breakfast differs from 10%. What are the values of the test statistic and P-value for this test?Find the z-table here.

A
z = StartStartFraction 0.167 minus 0.1 OverOver StartRoot StartFraction 0.1 (1 minus 0.1) Over 150 EndFraction EndEndFraction, p-value = 0.0066
Option A
B
z = StartStartFraction 0.167 minus 0.1 OverOver StartRoot StartFraction 0.167 (1 minus 0.167) Over 150 EndFraction EndEndFraction, p-value = 0.0278
Option B
C
z = StartStartFraction 0.167 minus 0.1 OverOver StartRoot StartFraction 0.1 (1 minus 0.1) Over 150 EndFraction EndEndFraction, p-value = 0.0033
Option C
D
z = StartStartFraction 0.167 minus 0.1 OverOver StartRoot StartFraction 0.167 (1 minus 0.167) Over 150 EndFraction EndEndFraction, p-value = 0.0139
Option D
9

A restaurant manager believes that a majority of customers who dine at his restaurant would rate the food as excellent. To investigate this belief, he sends an email survey to a random sample of 50 customers from the large list of customers who have signed up for his frequent diner club. To encourage the customers to complete the survey, he offers a $10 gift card upon completion of the survey. He receives 22 responses, of which 20 rated the food as excellent. He would like to know if these data provide convincing evidence that more than 50% of customers who dine at his restaurant would rate the food as excellent. Are the conditions for inference met?

A
Yes, the conditions for inference are met.
B
No, the 10% condition is not met.
C
No, the Large Counts Condition is not met.
D
No, the randomness condition is not met.
10

It is claimed that 95% of teenagers who have a cell phone never leave home without it. To investigate this claim, a random sample of 300 teenagers who have a cell phone was selected. It was discovered that 273 of the teenagers in the sample never leave home without their cell phone. One question of interest is whether the data provide convincing evidence that the true proportion of teenagers who never leave home without a cell phone is less than 95%. The standardized test statistic is z = –3.18 and the P-value is 0.0007. What decision should be made using the = 0.01 significance level?

Question illustration
A
Reject H0 because the P-value is less than = 0.01.
Option A
B
Reject H0 because the test statistic is less than = 0.01.
Option B
C
Fail to reject H0 because the P-value is greater than = 0.01.
Option C
D
Fail to reject H0 because the test statistic is greater than = 0.01.
Option D

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