Chapter 9: Hypothesis Testing with Two Samples
Chapter 9 Homework
9.1 Homework
DIRECTIONS: For each of the word problems, use a solution sheet to do the hypothesis test. The solution sheet is found in Appendix E. Please feel free to make copies of the solution sheets. For the online version of the book, it is suggested that you copy the .doc or the .pdf files.
Note
If you are using a Student’s t-distribution for a homework problem in what follows, including for paired data, you may assume that the underlying population is normally distributed. (When using these tests in a real situation, you must first prove that assumption, however.)
The mean number of English courses taken in a two–year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from 29 males and 16 females. The males took an average of three English courses with a standard deviation of 0.8. The females took an average of four English courses with a standard deviation of 1.0. Are the means statistically the same?
A student at a four-year college claims that mean enrollment at four–year colleges is higher than at two–year colleges in the United States. Two surveys are conducted. Of the 35 two–year colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 4,777. Of the 35 four-year colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191.
Solution
Subscripts: 1: two-year colleges; 2: four-year colleges
- H0: μ1 ≥ μ2
- Ha: μ1 < μ2
- [latex]{\overline{X}}_{1}–{\overline{X}}_{2}[/latex] is the difference between the mean enrollments of the two-year colleges and the four-year colleges.
- Student’s-t
- test statistic: -0.2480
- p-value: 0.4019
- Check student’s solution.
- Alpha: 0.05
- Decision: Do not reject
- Reason for Decision: p-value > alpha
- Conclusion: At the 5% significance level, there is sufficient evidence to conclude that the mean enrollment at four-year colleges is higher than at two-year colleges.
At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis.
| Relaxed time (seconds) | Jumping time (seconds) |
|---|---|
| 26 | 21 |
| 47 | 40 |
| 30 | 28 |
| 22 | 21 |
| 23 | 25 |
| 45 | 43 |
| 37 | 35 |
| 29 | 32 |
Mean entry-level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. A recruiting office thinks that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. The recruiting office randomly surveys 50 entry level mechanical engineers and 60 entry level electrical engineers. Their mean salaries were 💲46,100 and 💲46,700, respectively. Their standard deviati