a battery manufacturer believes there is a difference in the longevity of one-time use and rechargeable batteries. Employees who work in the research and development department created 5 different pairs of batteries, making one of each type. Then, the employees put the batteries under a performance test and measured the time it took for them to fail. The results (in days until failure) are shown below. Note: D=(one time use batteries-rechargeable batteries)

One time use Rechargeable

batteries (days batteries (days

until failure) until failure)

40 45

42 49

39 46

38 48

43 49

Assume that both of the populations are normally distributed. At the 0.05 level of significance, is there sufficient evidence to show that there is a change in the average time until failure between one-time use and rechargeable batteries?

Complete the steps for this hypothesis test to determine a conclusion and interpret the results.