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. They obtained the following data:

1,973 4,838 3,805 4,494 4,738 5,249 4,459 4,098 4,722 5,894 3,322 4,800

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 the managers reach based on these sample data?

Be sure to examine the required normality assumption.