Econ 310, Spring 2014- Week 12:
Problem 1 - You are conducting a poll for a hat company in preparation for the upcoming holiday season. The company wants you to determine whether women are more likely than men to shop for hats. In your poll, 26 percent of men and 34 percent of women said that they were planning on purchasing hats.
1. What additional pieces of information do you need to conduct a hypothesis test?
2. Suppose that the sample size for men is 296 and the sample size for women is 282. Construct a test statistic. What do you conclude?
3. Construct a 95% confidence interval.
4. Now assume that if women are 5 percent points more likely to purchase hats than men, then the store will run a special female targeted promotion. Will you advise them to run the promotion.
Problem 2- Continuing with the previous example, the hat company now wants to get a sense of how many hats men and women will purchase. So they commission a new survey, this time asking the respondents how many hats they purchased last year. They survey 200 men and 200 women, with men purchasing on average 2.2 hats and women purchasing 1.8 hats (with accompanying estimated standard deviation of 2.3 and 2 respectively)
1. Construct a hypothesis test to determine whether these sample have different means while assuming different population variance.
2. Construct a 95% confidence interval
3. Repeat previous two questions while assuming equal population variance.
4. Construct a hypothesis test on whether the variances of the two populations are different, i.e., σ12/σ22 = 1 or not.
Now suppose that in addition to gender, the survey also included the zip code of the respondent's residence. From this you are able to compute temperature of where the respondent lives, and you decide to group the respondents accordingly. You decide to group the respondents based on the average temperatures of their residence. After doing so, you compute the paired mean and standard deviation, computed x-D = 0.10, sD = 0.80.
1. Construct a hypothesis test to determine whether these samples have different means
2. Construct a 95% confidence interval.
3. How does your conclusion differ after taking into account differences in temperature?