Question

Researchers wondered if there was a difference between males and females in regard to some common annoyances. They asked a random sample of males and​ females, the following​ question: "Are you annoyed by people who repeatedly check their mobile phones while having an​ in-person conversation?" Among the

517

males​ surveyed,

155

responded​ "Yes"; among the 589

females​ surveyed,205

responded​ "Yes." Does the evidence suggest a higher proportion of females are annoyed by this​ behavior? Complete parts​ (a) through​ (g) below.

Answer 1

Let p1 and p2 be the proportions of males and females respectively which are annoyed by people who repeatedly check their mobile phones while having an​ in-person conversation.

Null hypothesis H0: p1 = p2

Alternative hypothesis H1: p1 < p2

For this analysis, let the significance level be 0.05. The test method is a two-proportion z-test.

p1 = 155/517 = 0.2998066

p2 = 205 / 589 = 0.3480475

Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

p = Total People who responded Yes / Total people surveyed = (155 + 205) / (517 + 589) = 0.3254973

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] } where n1, n2 are the sample size for males and females respectively.

SE = sqrt{ 0.3254973 * ( 1 - 0.3254973 ) * [ (1/517) + (1/589) ] } =  0.02823841

Test statistic, z = (p2 - p1) / SE = (0.3480475 - 0.2998066) / 0.02823841 = 1.708343

P-value = P(z > 1.708343) = 0.04378636

As, p-value is less than the significance level of 0.05, we reject H0 and conclude that there is significant evidence that proportion of females annoyed by this​ behavior are higher as compared with proportion of men.

Note - if the significance level is 0.01, then p-value is greater than the significance level of 0.05, we fail to reject H0 and conclude that there is no significant evidence that proportion of females annoyed by this​ behavior are higher as compared with proportion of men.