Question

A sample of 500 shoppers was selected in a large metropolitan are to determine various information concerning consumer behavior. Among the questions asked was, “Do you enjoy shopping for clothing?” Of the 240 males, 136 said yes. Of 260 females, 224 answered yes.
a) Is there evidence of a significant difference between males and females in the proportion who enjoy shopping for clothing at the 0.01 level of significance?
b) Find the p-value in (a) and interpret its meaning
c) Construct and interpret a 95% confidence interval estimate of the difference between the proportion of males and females who enjoy shopping for clothing.
d) What are your answers to (a) through (c) if 206 males enjoyed shopping for clothing?

Answer 1

A sample of 500 shoppers was selected in a large metropolitan are to determine various information concerning consumer behavior. Among the questions asked was, “Do you enjoy shopping for clothing?” Of the 240 males, 136 said yes. Of 260 females, 224 answered yes. a) Is there evidence of a significant difference between males and females in the proportion who enjoy shopping for clothing at the 0.01 level of significance? ---- Sample Proportions: men: 136/240 = 17/30 women: 224/260 = 56/65 --------------------------------- Ho: proportions are the same Ha: they are different --- I ran a 2-Prop Z-Test and got the following: test statistic: z = -7.34 p-value: 2.207x10^-13 ---------- Conclusion: Since the p-value is < 1%, Reject Ho. ---------------------------------------------------------------- b) Find the p-value in (a) and interpret its meaning Approximately 0.0000000000002207 of test results would have given stronger evidence for rejecting Ho. ---------------------------------------------------------------- c) Construct and interpret a 95% confidence interval estimate of the difference between the proportion of males and females who enjoy shopping for clothing. sample proportion difference: 17/30 - 56/65 = -0.2949 standard error: 1.96*sqrt[(17/30)(13/30)/240 + (56/65)(9/65)/260]= 0.0755 95% CI: -0.2949-0.0755 < p(men)-p(women) < -0.2949+0.0755 =================================================================== d) What are your answers to (a) through (c) if 206 males enjoyed shopping for clothing? I'll leave that one to you. ===================================== Cheers, Stan H.