Dynacel batteries last 13.15 hours in a standard flashlight, on average. Dynacel engineers have developed a new manufacturing process that they hope will increase the mean life of their batteries. They will test a random sample of batteries to determine if the new process has indeed increased the average life of the batteries.

1. 38 batteries made by the new process are randomly selected and tested.To test at 1% significance, what is the critical t-score (3 decimal places)?
2. The new batteries had a mean life of 14.57 hours with a standard deviation of 3.5 hours.Calculate the test statistic for the sample (round to 3 decimal places).
3. What is the test conclusion?

A. Reject the null hypothesis: The test provides evidence that the mean is greater than 13.15 hours.

B. Reject the alternative hypothesis: The test provides sufficient evidence to show the mean is not greater than 13.15 hours.

C. Accept the null hypothesis: The test shows that the mean is 13.15 hours.

D. Accept the alternative hypothesis: The test shows that the mean is 14.57 hours.

E. Don't reject the null hypothesis: The test does not provide sufficient evidence to prove the mean is greater than 13.15 hours.