1. Confidence Interval:
Compute a 95% confidence interval for the population mean, based on the sample numbers 21, 22, 33, 34, 25, 26, and 139.
Change the last value to 29 and re-compute the confidence interval.
What is an outlier and how does it affect the confidence interval?
2. Confidence Interval:
A sample from a normal population has size = 109 observations, mean = 7.99, and standard deviation = 3.67. What is the 95 percent confidence interval for the population mean? Use the Excel function, =CONFIDENCE.NORM() and the mean to find the two limits.
3. Confidence Limit:
The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester. A sample of 25 students enrolled in the university indicates that x(bar) = $315.40 and s = $43.20.
a. Using the .10 level of significance, is there evidence that the population mean is above $300?
b. What is your answer if x(bar) = $315.40, s = $75.00, and the level of significance is 0.05?
c. What is your answer if x(bar) = $305.11, s = $43.20, and the level of significance is 0.10?
d. D. Based on the information in part a, what decision should the director make about the books used for the courses if the goal is to keep the cost below $300?
4. t-Test: Paired Two Sample for Means
In week 7 we will study Hypothesis Testing in detail.
For answering the following question, you need a brief idea of what hypothesis testing is.
Please read the following introduction:
https://www.socialresearchmethods.net/kb/hypothes.php
The director for Weight Watchers International wants to determine if the changes in their program results in better weight loss. She selected 25 Weight Watcher members at random and compared their weight 6 months later to weight at the start of the program. Here are the results: (The weight in the column labeled "After" represents their weights six months later and "Before" represents their weight at the start of the six-month period.) The director used .05 as the significance level.
Use Excel to test H0: After - Before ≥ 0 vs. HA: After - Before < 0.
For each paired difference, compute After - Before. In Data Analysis, t-Test: Paired Two Sample for means, select the After data for Variable 1 Range. Note that the critical value output by Data Analysis for this test is always positive. In this problem, the sign of the critical value is negative corresponding to a 1-tailed test with lower reject region and negative lower critical value. State your conclusion.
| Person |
Before |
After |
| 1 |
176 |
164 |
| 2 |
192 |
191 |
| 3 |
185 |
176 |
| 4 |
177 |
176 |
| 5 |
196 |
185 |
| 6 |
178 |
169 |
| 7 |
196 |
196 |
| 8 |
181 |
172 |
| 9 |
158 |
158 |
| 10 |
201 |
193 |
| 11 |
191 |
185 |
| 12 |
193 |
189 |
| 13 |
176 |
175 |
| 14 |
212 |
210 |
| 15 |
177 |
173 |
| 16 |
183 |
180 |
| 17 |
210 |
204 |
| 18 |
198 |
192 |
| 19 |
157 |
152 |
| 20 |
213 |
200 |
| 21 |
161 |
161 |
| 22 |
177 |
166 |
| 23 |
210 |
203 |
| 24 |
192 |
186 |
| 25 |
178 |
170 |