Suppose a survey of 899 college students who were asked about their smoking behavior. Of the students surveyed, 262 classified themselves as nonsmokers, but said "yes" when asked later in the survey if they smoked. These students were classified as "phantom smokers," meaning that they did not view themselves as smokers even though they do smoke at times. The authors were interested in using these data to determine if there is convincing evidence that more than 25% of college students fall into the phantom smoker category. Suppose that the sample of 899 college students can be regarded as representative of college students in the United States. (a) What hypotheses would you test to answer the question posed? H0: p = 0.25 versus Ha: p ≠ 0.25 H0: p ≠ 0.25 versus Ha: p = 0.25 H0: p = 0.25 versus Ha: p > 0.25 H0: p < 0.25 versus Ha: p > 0.25 H0: p = 0.25 versus Ha: p < 0.25 (b) Is the sample size large enough for a large-sample test for a population proportion to be appropriate? YesNo (c) What is the value of the test statistic and the associated P-value for this test? (Use a table or SALT. Round your test statistic to two decimal places and your P-value to four decimal places.) z=P-value= (d) If a significance level of 0.05 were chosen, would you reject the null hypothesis or fail to reject the null hypothesis? Reject H0.Fail to reject H0.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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Question

Suppose a survey of 899 college students who were asked about their smoking behavior. Of the students surveyed, 262 classified themselves as nonsmokers, but said "yes" when asked later in the survey if they smoked. These students were classified as "phantom smokers," meaning that they did not view themselves as smokers even though they do smoke at times. The authors were interested in using these data to determine if there is convincing evidence that more than 25% of college students fall into the phantom smoker category. Suppose that the sample of 899 college students can be regarded as representative of college students in the United States.

(a)

What hypotheses would you test to answer the question posed?

H₀: p = 0.25

versus

H_a: p ≠ 0.25

H₀: p ≠ 0.25

versus

H_a: p = 0.25

H₀: p = 0.25

versus

H_a: p > 0.25

H₀: p < 0.25

versus

H_a: p > 0.25

H₀: p = 0.25

versus

H_a: p < 0.25

(b)

Is the sample size large enough for a large-sample test for a population proportion to be appropriate?

YesNo

(c)

What is the value of the test statistic and the associated P-value for this test? (Use a table or SALT. Round your test statistic to two decimal places and your P-value to four decimal places.)

z=P-value=

(d)

If a significance level of 0.05 were chosen, would you reject the null hypothesis or fail to reject the null hypothesis?

Reject H₀.Fail to reject H₀.

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