Assignment:
Sigman Corporation makes batteries that are used in highway signals in rural areas. The company managers claim that the median life of a battery exceeds 4,000 hours. To test this claim, they have selected a random sample of n = 12 batteries and have traced their life spans between installation and failure. The following data were obtained:
| 1973 |
4838 |
3805 |
4494 |
4738 |
5249 |
| 4459 |
4098 |
4722 |
5894 |
3322 |
4800 |
a. State the appropriate null and alternative hypotheses.
b. Assuming that the test is to be conducted using a 0.05 level of significance, what conclusion should be reached based on these sample data? Be sure to examine the required normality assumption.
Provide complete and step by step solution for the question and show calculations and use formulas.