Question: Is the proportion of men who write a shopping list before going shopping less than the proportion of women who do so? Let p1 and p2 represent the population proportions of men and women, respectively, who use shopping lists. Suppose that a random sample of 50 men and 50 women were asked if they use a shopping list when they have more than ten items to buy. Of the 50 men, 20 said yes and of the 50 women, 30 said yes.
a. Write the null and alternative hypotheses in terms of p1 and p2, taking into account the initial question asked at the beginning of this exercise.
b. Provide numerical values for p^1 and p^2.
c. To find the null standard error, the combined sample proportion p^ is required. Compute p^ for this situation.
d. Find the test statistic for this situation.
e. Form a conclusion using the .05 level of significance.