Explanation Calculation: In the survey, out of 737 current smokers, 295 indicated that they believed they have a higher than average risk of cancer. Step 1: Population characteristic of interest: Let p be the population characteristic of interest. In this context, p denotes population proportion of smokers who view themselves as being at increased risk of cancer. Step 2: Null hypothesis: H 0 : p = 0.5 That is, there is no convincing evidence that the proportion of all smokers who view themselves as being at increased risk of cancer is in fact less than 0.5. Step 3: Alternative hypothesis: H a : p < 0.5 That is, there is convincing evidence that the proportion of all smokers who view themselves as being at increased risk of cancer is in fact less than 0.5. Step 4: Significance level, α : It is given that the significance level, α = 0.05 . Step 5: Test statistic, z : z = p ^ − p p ( 1 − p ) n , Where, p ^ is the sample proportion, p be the hypothesized proportion and n is the sample size. Substitute the hypothesized proportion, p = 0.5 in the test statistic, z = p ^ − 0.5 0.5 ( 1 − 0.5 ) n Here, the sample proportion p ^ is not known. Step 6: Assumptions: Let p ^ be the sample proportion, which is selected from a random sample. The large sample z test can be used if the sample size n satisfies the below conditions: n ( hypothesized value ) ≥ 10 and n ( 1 − hypothesized value ) ≥ 10 . The sample size should not be greater than 10% of the population size. Requirement check: It is assumed that the sample is from a random sample. Check the conditions: n ( hypothesized value ) ≥ 10 and n ( 1 − hypothesized value ) ≥ 10 . n ( hypothesized value ) = n p = 737 ( 0

Introduction to Statistics and Data Analysis

5th Edition

ISBN: 9781305750999

Author: Peck Olson Devore

Publisher: CENGAGE C

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Chapter 10, Problem 72CR

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Chapter 10 Solutions

Introduction to Statistics and Data Analysis

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Check whether there is convincing evidence that the proportion of all smokers who view themselves as being at increased risk of cancer is in fact less than 0.5.

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Check whether there is convincing evidence that the proportion of all smokers who view themselves as being at increased risk of cancer is in fact less than 0.5.

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