Question 1.
The time to failure in hours of an electronic component subjected to an accelerated life test is shown in the following table. To accelerate the failure test, the units were tested at an elevated temperature (read down, then across).
| Electronic | Component | Failure | Time |
| 127 | 124 | 121 | 118 |
| 125 | 123 | 136 | 131 |
| 131 | 120 | 140 | 125 |
| 124 | 119 | 137 | 133 |
| 129 | 128 | 125 | 141 |
| 121 | 133 | 124 | 125 |
| 142 | 137 | 128 | 140 |
| 151 | 124 | 129 | 131 |
| 160 | 142 | 130 | 129 |
| 125 | 123 | 122 | 126 |
Suppose you want to test whether the failure time is equal to 135. Given the significance level set at 5%, do the following to conduct a t-test.
- Set up the null and alternative hypothesis (two-tailed).
- Calculate the test statistic.
- Compare the test statistic to a critical value at the 5% significance level and determine if the null hypothesis should be rejected.
- Discuss your results using non-technical language.
Question 2.
Rubber can be added to asphalt to reduce road noise when the material is used as pavement. The data shows the stabilized viscosity (cP) of 15 specimens of asphalt paving material. To be suitable for the intended pavement application, the mean stabilized viscosity should be equal to 3200. Test this hypothesis using a t-test and the 5% significance level.
Stabilized Viscosity of Rubberized Asphalt
| Specimen | Stabilized Viscosity |
| 1 | 3,193 |
| 2 | 3,124 |
| 3 | 3,153 |
| 4 | 3,145 |
| 5 | 3,093 |
| 6 | 3,466 |
| 7 | 3,355 |
| 8 | 2,878 |
| 9 | 3,182 |
| 10 | 3,227 |
| 11 | 3,256 |
| 12 | 3,332 |
| 13 | 3,204 |
| 14 | 3,282 |
| 15 | 3,170 |
- Set up the null and alternative hypothesis (two-tailed).
- Calculate the test statistic.
- Compare the test statistic to a critical value at the 5% significance level and determine if the null hypothesis should be rejected.
- Discuss your results using non-technical language.
