section 10.1
1. Assume that a sample of differences for the matched pairs in the table follows a normal distribution, and perform Steps (a) and (b).
| Subject | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Sample 1 | 100.7 | 110.2 | 105.3 | 107.1 | 95.6 | 109.9 | 112.3 | 94.7 |
| Sample 2 | 104.4 | 112.5 | 105.9 | 111.4 | 99.8 | 109.9 | 115.7 | 97.7 |
10.99.1
(a) , (b) (–4.0376, –1.3374)
2. For the data in Exercise 1, test whether , using the critical-value method and level of significance .
3. For the data in Exercise 1, test whether , using the -value method and level of significance .
10.99.3
. Reject if . . Since the , we reject . There is evidence that the population mean of the differences is less than 0.
section 10.2
Refer to the following summary statistics for two independent samples for Exercises 4–7.
| Sample 1 | |||
| Sample 2 |
4. We are interested in constructing a 95% confidence interval for . Explain why it is appropriate to do so.
5. Provide the point estimate of the difference in population means .
10.99.5
0.1
6. Calculate the margin of error for a confidence level of 95%.
7. Construct and interpret a 95% confidence interval for .
10.99.7
(0.094, 0.106). We are 95% confident that the interval captures the difference in population means.
8. A random sample of 49 young persons with college degrees had a mean salary of $30,000 with a standard deviation of $5000. An independent random sample of 36 young persons without college degrees had a mean salary of $25,000 and a standard deviation of $4000.
section 10.3
9. The Centers for Disease Control, in their Pregnancy Risk Assessment Monitoring System, reported that 641 of 823 new mothers living in Florida and 658 of 824 new mothers living in North Carolina took their babies in for a checkup within one week of delivery.22
10.99.9
(a) (–0.0715, 0.0322) (b) Since the is not ≤ 0.01, we do not reject . There is insufficient evidence that the population proportion of new mothers in Florida who took their babies in for a checkup within one week of delivery is different from the proportion of new mothers in North Carolina who took their babies in for a checkup within one week of delivery.
629
section 10.4
For Exercises 10 and 11, assume that the populations are normally distributed. Perform the indicated hypothesis tests using the critical-value method.
10.
11.
10.99.11
.. Reject if . . Since is ≤ 0.6173, we reject . There is evidence at the level of significance that the population standard deviation of Population 1 is less than the population standard deviation of Population 2.
For Exercises 12 and 13, assume that the populations are normally distributed. Perform the indicated hypothesis tests using the -value method for each exercise.
12.
13.
10.99.13
. Reject if the . . . Since the is ≤ 0.01, we reject . There is evidence at the level of significance that the population standard deviation of Population 1 is less than the population standard deviation of Population 2.