STAT177 homework sheet #6

1) For each of the following scenarios state which test to conduct. Choose from Z-test, t-test assuming equal variances, t-test assuming unequal variances, paired t-test, Mann-Whitney test or Wilcoxon test.

a) A survey is conducted in Calgary and Edmonton to see if there is any significant difference in the average amount people spend eating out. They pull equal sample sizes of 200 for each city. Analysis of the data indicates that both samples are normally distributed. (Z test)

b) A teacher wanted to compare marks between her two classes. She has 25 students in one class and 28 in the other. When she checked to see if the data was normally distributed, she found that the marks for both classes were heavily skewed left. (Mann-Whitney)

c) A store did a shopper-intercept survey in a mall asking 100 people to rate 2 new logos on a scale from 1 to 5, 5 being best. (Wilcoxon)

d) A store wanted to compare average daily sales at 2 of its locations. They took samples of 10 daily sales from both stores (the dates were independently chosen for each store). Analysis indicated the standard deviations were equal and that the data followed a normal distribution. (t-test assuming equal variances)

e) A store ran an identical ad campaign at 2 of its locations. It then sampled the same 10 days of data from both stores in order to compare average sales between the stores. Analysis indicated the data followed a normal distribution. (paired t-test)

A tourist magazine wanted to compare daily rates between inner city hotels and those in the suburbs to see if there was any significant difference. It sampled 12 from each type. These were the results:

Downtown	597	400	602	309	292	458	452	484	492	753	421	777
Suburbs	429	531	475	519	479	458	469	499	468	482	435	472

2) State the null and alternative hypotheses. (Ha: mean(downtown) ¹ mean(suburbs))

3) Based on the results, is there any significant difference in the average daily rate between downtown and suburbs? (p-value = 0.567; conclude no significant difference)

A hostel underwent some renovations to see if it could improve the average rating on its cards. It used a scale of 1 to 5 where 1 = poor and 5 = excellent. It sampled 8 cards from both before and after the renovations. It assumed that the cards were all filled out by different visitors. These were the results:

Before	3	2	3	4	4	3	2	2
After	4	4	5	3	4	3	4	4

4) State the null and alternative hypotheses (Ha: median(after) >median(before))

5) What is the appropriate test? (Mann-Whitney)

6) Based on the analysis, are the ratings improved? Test at 5%. (Test statistic = 88; conclude the ratings are improved.)

7) Suppose these were ratings by repeat visitors who rated the hostel both before and after the renovations. What would be the appropriate test? (Wilcoxon)

8) Based on the assumptions in question 7, what would the hostel management now conclude? Test at 5%. (Test statistic = 1.5; same conclusion)

A store introduced a new loyalty program to see if it would result in higher sales. After 6 months, it held focus groups with 8 of its most loyal customers and asked them to compare their spending before the program began to after. These were the results:

	Before	After
Store #1	270	359
Store #2	322	348
Store #3	293	340
Store #4	306	337
Store #5	294	354
Store #6	278	367
Store #7	281	373
Store #8	288	321

9) What is the appropriate test? (paired t-test)

10) Based on the results, is the new loyalty program effective? Test at 5%. (p-value = 0; conclude the program is effective)

11) Suppose a level of significance had not been set. Why would the same conclusion be reached? (p-value is less than 1% using the general rule of thumb)

From the text, read:

Chapter 5, pages 77-93 (to end of Wilcoxon test)