Question

manufacturer of batteries wanted to test the longevity of one-time-use and rechargeable batteries. Employees who work in the research and development department created 10 different pairs of battery, making one of each type. Then they put the batteries under a performance test and measured the time it took for them to fail. Assume that the populations are normally distributed.

The manufacturer tests the paired data, where α=0.05, in order to evaluate the claim that the true mean difference in times until failure between one-time-use and rechargeable batteries is not equal to zero.

For this test: H0:μd=0, Ha:μd≠0, which is a two-tailed test.

The test results are: t≈−1.87 , p-value is approximately 0.094

Which of the following are appropriate conclusions for this hypothesis test? Select all that apply.

• There is not sufficient evidence at the α=0.05 level of significance to conclude that the true mean difference in times until failure between one-time-use and rechargeable batteries is not equal to zero.

• There is sufficient evidence at the α=0.05 level of significance to conclude that the true mean difference in times until failure between one-time-use and rechargeable batteries is not equal to zero.

• Reject the null hypothesis that the true mean difference in times until failure between one-time-use and rechargeable batteries is equal to zero.

• Fail to reject the null hypothesis that the true mean difference in times until failure between one-time-use and rechargeable batteriesis equal to zero.

Answer 1

Since p-value > alpha(0.05), we fail to reject the null hypothesis and there is not sufficient evidence to conclude that that the true mean difference in times until failure between one-time-use and rechargeable batteries is not equal to zero.

Correct option

There is not sufficient evidence at the α=0.05 level of significance to conclude that the true mean difference in times until failure between one-time-use and rechargeable batteries is not equal to zero.

Fail to reject the null hypothesis that the true mean difference in times until failure between one-time-use and rechargeable batteriesis equal to zero.