Five questions - all equally weighted.
QUESTION 1
In a recent study of 45 college students who own Nike running shoes, the following data were gathered that shows light, medium, and heavy users broken down by gender.
|
USAGE
|
FEMALE
|
MALE
|
ROW TOTAL
|
|
Light Users
|
12
|
5
|
17
|
|
Medium Users
|
7
|
5
|
12
|
|
Heavy Users
|
5
|
11
|
16
|
|
COLUMN TOTAL
|
24
|
21
|
45
|
Is there a relationship between gender and usage?
- State the null and alternate hypotheses.
The null hypotheses is that there is no relationship between gender and usage.
The alternative hypotheses is that there is a relationship between gender and usage
- Conduct the appropriate statistical test to test these hypotheses.
N-way An ova
- Did you find a significant relationship between gender and usage? Hint: The tabled chi-squared statistic for 0.05 significance and 2 degrees of freedom is 5.991.
QUESTION 2
| Number |
Thousands of Dollars |
Count in Thousands |
by Region |
| STORE |
SALES |
TRAFFIC |
REGION |
| 1 |
1021 |
62 |
N |
| 2 |
622 |
35 |
N |
| 3 |
693 |
36 |
N |
| 4 |
1204 |
72 |
N |
| 5 |
850 |
41 |
N |
| 6 |
790 |
39 |
N |
| 7 |
929 |
49 |
N |
| 8 |
493 |
25 |
N |
| 9 |
772 |
41 |
N |
| 10 |
801 |
39 |
N |
| 11 |
854 |
35 |
S |
| 12 |
568 |
27 |
S |
| 13 |
921 |
55 |
S |
| 14 |
699 |
38 |
S |
| 15 |
497 |
24 |
S |
| 16 |
657 |
28 |
S |
| 17 |
1009 |
53 |
S |
| 18 |
976 |
55 |
S |
| 19 |
844 |
33 |
S |
| 20 |
821 |
29 |
S
|
Refer to the FINAL EXAM TRAFFIC COUNTS Excel spreadsheet. Twenty stores in a statewide retail chain are surveyed. The table shows the total number of sales per store (expressed in thousands of dollars) and also the traffic count (number of cars that pass the store per day, expressed in thousands). The table also shows whether the store is located in the north or south regions of the country.
Do sales depend on traffic count? On region of the country (north or south)? On both?
- State the null and alternate hypotheses.
The null hypothesis is that there is not a significant relationship between traffic and region of country.
The alternative hypothesis is there is a significant difference between one of two hypothesis.
- Conduct the appropriate statistical test to test these hypotheses.
N-way Anova
- Did you find a significant relationship between sales and traffic count? If yes, carefully interpret the coefficient you obtained, in plain English.
- Did you find a significant relationship between sales and region of the country. If yes, carefully interpret the coefficient you obtained, in plain English.
- What percentage of the variation in sales is accounted for in your best model? How do you know?
QUESTION 3
| ANOVA PROBLEM (independent means) |
| Store |
Plastic |
Metal |
Paper Bag |
| 1 |
432 |
365 |
123 |
| 2 |
360 |
405 |
150 |
| 3 |
397 |
396 |
140 |
| 4 |
408 |
390 |
102 |
| 5 |
417 |
404 |
150 |
| 6 |
380 |
372 |
151 |
| 7 |
422 |
378 |
123 |
| 8 |
406 |
410 |
160 |
| 9 |
400 |
383 |
125 |
| 10 |
408 |
400 |
178 |
|
|
Refer to the FINAL EXAM ANOVA Excel spreadsheet. Thirty hardware stores are included in a study of customer behaviors regarding different containers for paint. The company is trying out plastic and metal containers, as well as a novel idea in paint packaging: selling it in a plain brown paper bag. Ten stores are assigned randomly to each type of container and the number of units of paint sold in a given week in each store is recorded. The table shows the number of units of paint sold in the test week per store.
Do sales depend on type of container? If so, which containers are significantly better or worse?
- State the null and alternate hypotheses. (Plain English is OK, no need for equations).
- Conduct the appropriate Analysis of Variance test to test these hypotheses.
- Did you find a significant difference among the containers? If yes, carefully explain your findings, to the best of your abilities.
QUESTION 4
You want to determine the average amount spent by campers on food at a local state campsite. You would like your estimate to be within plus or minus $20 of the true population value. You would like 95% confidence in the interval you calculate, so you will use z = 1.96 (the correct z value for 95% confidence). You go through the last few years of estimates and you discover that the historic variation in expenditures on food, as measured by standard deviation s is 100.
- What sample size would you recommend so that you can achieve your confidence and precision goals?
- If you wanted to increase confidence to 99%, how much does your required sample size change? (for 99%, use z = 2.575)
- Now, reset confidence to 95%. If you wanted to double the precision (that is, get MORE precise), how much does your required sample size change?
QUESTION 5
You want to see if there is a difference among juniors and seniors at your university in ownership of the latest version of the iPad. You conduct a study of 300 juniors and 300 seniors, and you discover the following: 45 of the juniors have the latest iPad, and 60 of the seniors have the latest iPad.
Is there a significant difference between juniors and seniors in terms of the proportion that have the latest iPad?
- State the null and alternate hypotheses.
Null hypothesis: More seniors have more ipads than the juniors in relation to the age difference
Alternative hypothesis: Less seniors have less ipads due to the less need o listen to music compared to the seniors.
- Conduct the appropriate statistical test to test these hypotheses.
- Did you find a significant difference between juniors and seniors? If yes, carefully explain your findings.