Secondhand stores. Shopping at secondhand stores is becoming more popular and has even attracted the attention of business schools. A study of customers' attitudes toward secondhand stores interviewed samples of shoppers at two secondhand stores of the same chain in two cities. The breakdown of the respondents by gender is as follows:
|
Gender
Men
|
City 1
38
|
City 2
68
|
|
Women
|
203
|
150
|
|
Total
|
241
|
218
|
Is there a signi?cant difference between the proportions of women customers in the two cities?
(a) State the null hypothesis, ?nd the sample proportions of women in both cities, do a two-sided z test, and give a P-value using Table A.
(b) Calculate the X2 statistic and show that it is the square of the z statistic. Show that the P-value from Table F agrees (up to the accuracy of the table) with your result from (a).
(c) Give a 95% con?dence interval for the difference between the proportions of women customers in the two cities.