Explanation The test hypotheses are given as follows: Denote p 1 as the proportion of subjects judging automobile 1 and p 2 as the proportion of subjects judging automobile 2. Null hypothesis: H 0 : p 1 = p 2 That is, the proportion of subjects judging automobile 1 is the same as the proportion of subjects judging automobile 2. Alternative hypothesis: H a : p 1 > p 2 That is, the proportion of subjects judging automobile 1 is greater than the proportion of subjects judging automobile 2. Test statistic: The test statistic is given below: Z = p ^ 1 − p ^ 2 p 1 ( 1 − p 1 ) n 1 + p 2 ( 1 − p 2 ) n 2 Here, p ^ 1 and p ^ 2 are the sample proportions, Y 1 and Y 2 are the number of observations of interest, and n 1 and n 2 are the sample sizes of two population. The pooled estimate, p ^ , is obtained as follows: Substitute Y 1 as 37, Y 2 as 23, n 1 as 50, and n 2 as 50. p ^ = n 1 p ^ 1 + n 2 p ^ 2 n 1 + n 2 = Y 1 + Y 2 n 1 + n 2 = 37 + 23 50 + 50 = 60 100 = 0

Mathematical Statistics with Applications

7th Edition

ISBN: 9781133384380

Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Publisher: Cengage Learning US

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Chapter 10.6, Problem 58E

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State whether the result provides the sufficient evidence that a female model increases the perceived cost of an automobile at α=0.05 level test.

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Mathematical Statistics with Applications

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State whether the result provides the sufficient evidence that a female model increases the perceived cost of an automobile at α = 0.05 level test.

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State whether the result provides the sufficient evidence that a female model increases the perceived cost of an automobile at α=0.05 level test.

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