A dietician read in a survey that 76.4% of adults in the U.S. do not eat breakfast at least 2 days a week. She believes that a smaller proportion skip breakfast 2 days a week. To verify her claim, she selects a random sample of 75 adults and asks them how many days a week they skip breakfast. 55 of them report that they skip breakfast at least 2 days a week. Test her claim at a = 0.01. The correct hypotheses would be:

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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ISBN:9780547587776
Author:HOLT MCDOUGAL
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Chapter11: Data Analysis And Probability
Section: Chapter Questions
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26

A dietician read in a survey that 76.4% of adults in the U.S. do not eat breakfast at least 2 days a week. She
believes that a smaller proportion skip breakfast 2 days a week. To verify her claim, she selects a random
sample of 75 adults and asks them how many days a week they skip breakfast. 55 of them report that they
skip breakfast at least 2 days a week. Test her claim at a = 0.01.
The correct hypotheses would be:
О Но:р < 0.764
HA:p > 0.764 (claim)
Но:р > 0.764
HA:p < 0.764 (claim)
O Ho:p = 0.764
HA:P + 0.764 (claim)
Since the level of significance is 0.01 the critical value is -2.326
The test statistic is:
(round to 3 places)
The p-value is:
(round to 3 places)
The decision can be made to:
O reject Ho
O do not reject Ho
The final conclusion is that:
There is enough evidence to reject the claim that a smaller proportion skip breakfast 2 days a week.
There is not enough evidence to reject the claim that a smaller proportion skip breakfast 2 days a
week.
There is enough evidence to support the claim that a smaller proportion skip breakfast 2 days a
week.
O There is not enough evidence to support the claim that a smaller proportion skip breakfast 2 days a
week.
Transcribed Image Text:A dietician read in a survey that 76.4% of adults in the U.S. do not eat breakfast at least 2 days a week. She believes that a smaller proportion skip breakfast 2 days a week. To verify her claim, she selects a random sample of 75 adults and asks them how many days a week they skip breakfast. 55 of them report that they skip breakfast at least 2 days a week. Test her claim at a = 0.01. The correct hypotheses would be: О Но:р < 0.764 HA:p > 0.764 (claim) Но:р > 0.764 HA:p < 0.764 (claim) O Ho:p = 0.764 HA:P + 0.764 (claim) Since the level of significance is 0.01 the critical value is -2.326 The test statistic is: (round to 3 places) The p-value is: (round to 3 places) The decision can be made to: O reject Ho O do not reject Ho The final conclusion is that: There is enough evidence to reject the claim that a smaller proportion skip breakfast 2 days a week. There is not enough evidence to reject the claim that a smaller proportion skip breakfast 2 days a week. There is enough evidence to support the claim that a smaller proportion skip breakfast 2 days a week. O There is not enough evidence to support the claim that a smaller proportion skip breakfast 2 days a week.
Expert Solution
Step 1

26

The claim of the test is that smaller proportion than 0.764 of skip breakfast 2 days a week. Let p be the population proportion of adults who do not eat breakfast at least 2 days a week.

Null hypothesis:

H0 : p0.764

Alternative hypothesis:

HA : p<0.764

Correct answer:

H0 : p0.764HA : p<0.764

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