Assignment:
Q1. The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the planwere recorded.
Was there a significant increase in the typical salesperson's weekly income due to the innovative incentive plan? Use the .05 significance level. Estimate the p-value, and interpret it.
| Salesperson |
before |
after |
| Sid Mahone |
$320 |
$340 |
| Carol Quick |
$290 |
$285 |
| Tom Jackson |
$421 |
$475 |
| Andy Jones |
$510 |
$510 |
| Jean Sloan |
$210 |
$210 |
| Jack Walker |
$402 |
$500 |
| Peg Mancuso |
$625 |
$631 |
| Anita Loma |
$560 |
$560 |
| John Cuso |
$360 |
$365 |
| Carl Utz |
|
$431 |
$431 |
| A. S. Kushner |
$506 |
$525 |
| Fern Lawton |
$505 |
$619 |
|
|
|
|
Q2. A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. A sample of 50 observations is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. Conduct the following test of hypothesis using the .08 significance level.
H?:μ1≤μ2
H1:μ1>μ2
a. Is this a one-tailed or a two-tailed test?
b. State the decision rule.
c. Compute the value of the test statistic.
d. What is your decision regarding H0?
e. What is the p-value?
Q3. A real estate developer is considering investing in a shopping mall on the outskirts of Atlanta, Georgia. Three parcels of land are being evaluated. Of particular importance is the income in the area surrounding the proposed mall. A random sample of four families is selected near each proposed mall. Following are the sample results. At the .05 significance level, can the developer conclude there is a difference in the mean income? Use the usual five-step hypothesis testing procedure.
| Southwyck Area |
Franklin Park |
Old Orchard |
| ($000) |
|
($000) |
|
($000) |
|
| 64 |
|
74 |
|
75 |
|
| 68 |
|
71 |
|
80 |
|
| 70 |
|
69 |
|
76 |
|
| 60 |
|
70 |
|
78 |
|
|
|
|
|
|
|
Q4. Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level.
a. State the null hypothesis and the alternate hypothesis.
b. What is the decision rule?
c. Compute SST, SSE, and SS total.
d. Complete an ANOVA table.
e. State your decision regarding the null hypothesis.
| treatment 1 |
treatment 2 |
treatment 3 |
| 3 |
|
9 |
|
6 |
|
| 2 |
|
6 |
|
3 |
|
| 5 |
|
5 |
|
5 |
|
| 1 |
|
6 |
|
5 |
|
| 3 |
|
8 |
|
5 |
|
| 1 |
|
5 |
|
4 |
|
|
|
4 |
|
1 |
|
|
|
7 |
|
5 |
|
|
|
6 |
|
|
|
|
|
4 |
|
|
|