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:

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.

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1.973 4.838 3.805 4.4 4.738 5.249 4.459 4,098 4.722 5.894 3,322 4,800