1. Thirty-eight 100-watt light bulbs were burned until all had failed; 21 were economy bulbs and 17 were premium bulbs. The time to failure of each bulb was observed. The economy bulbs gave a sample mean of 635.4 h and a sample standard deviation of 105.3 h. The premium bulbs gave a sample mean of 721.8 h and a sample standard deviation of 75.5 h. Can we conclude that the average life is longer for premium bulbs than for economy bulbs? State what assumptions you make and do what you can to test the assumptions. Support your conclusions with P-values.
2. Six individuals participated in a diet modification program to stimulate weight loss. Their weight in kg before and after the program is shown in the following table. One subject participated the study but moved away and was not available for an "After" weighing.
|
Subject: |
1 |
2 |
3 |
4 |
5 |
6 |
|
Before: |
88.5 |
97.0 |
112.2 |
91.4 |
85.0 |
95.5 |
|
After: |
89.1 |
88.5 |
100.4 |
86.3 |
* |
89.5 |
Is there evidence at the 5% level of significance that the program reduces mean weight? State what assumptions you make and do what you can to test the assumptions statistically.
3. In the following table, x = pressure of extracted gas (microns) and y = extraction time (min.).
|
x: |
40 |
155 |
260 |
325 |
420 |
|
y: |
2.5 |
3.1 |
3.6 |
3.9 |
5.0 |
Plot the data on a graph. Fit a simple linear regression model and add the fitted line to the graph. Use the analysis of variance procedure to test the hypothesis that the slope is zero. Find a two-sided 95% confidence interval for the residual variance s2. How could the design be improved if we wanted to test the assumption of linearity?