1) A consumer advocacy group feels that Walmart provides a less safe shopping environment than Target. To try to prove their point, they randomly selected 20 Walmart stores and found the annual number of crime reports filed for these stores. Each of these Walmart stores was then paired with a Target store within a 10 mile radius, and the annual crime reports for the associated Target stores were also recorded. The data is shown below. Test to to see if the mean number of crime incidents at Walmart stores is significantly larger than the mean number of crime incidents at Target stores. Please note the data shown below is not real, but if you would like to see the real example, check out walmartcrimereport.com. Unfortunately, the real data was collected in a way that was not fair to Walmart. Assume normality.
Summary statistics:
| Column | n | Mean | Variance | Std. dev. | Std. err. | Median | Range | Min | Max | Q1 | Q3 |
| Target |
20 |
781.55 |
21423.839 |
146.36885 |
32.729069 |
794 |
579 |
458 |
1037 |
657.5 |
856.5 |
| Walmart |
20 |
815.55 |
19975.418 |
141.33442 |
31.603337 |
832 |
549 |
493 |
1042 |
717 |
894 |
b) What is the test statistic? Give your answer to four decimal places.
c) Using a 0.05 level of significance, what is the critical point for this test? Give your answer to four decimal places.\
d) What is the appropriate conclusion?
2) Shortly after September 11th 2001, a researcher wanted to determine if the proportion of females that favored war with Iraq was significantly different from the proportion of males that favored war with Iraq. In a sample of 73 females, 28 favored war with Iraq. In a sample of 54 males, 29 favored war with Iraq.
b) What is the test statistic? Compute the statistic using male statistics subtracted from female statistics. Give your answer to four decimal places.
c) What is the P-value for the test? Give your answer to four decimal places.
d) Using a 0.01 level of significance, what conclusion should be reached?
e) What is the lower endpoint of a 99% confidence interval for the difference between the proportion of females that favor the war and the proportion of males that favor the war? Give your answer to four decimal places.
f) What is the upper endpoint of a 99% confidence interval for the difference between the proportion of females that favor the war and the proportion of males that favor the war? Give your answer to four decimal places.