Question 2 From past records it is known that the average life of a battery used in a digital clock is 305 days. The lives of the batteries are normally distributed. The battery was recently modified...

Question 2

From past records it is known that the average life of a battery used in a digital clock is 305 days. The lives of the batteries are normally distributed. The battery was recently modified to last longer. A sample of 40 modifed batteries was tested. It was discovered that the mean life was 311 days, and the sample standard deviation was 22 days. At the 0.01 level of sigificance, did the modofication increase the mean life of the battery?

(a) State the null and alternative hypotheses for this test.

(b) Compute the value of the Test Statistic?

(c) State the critical region for this test.

(d) State the conclusion for the test. Give reasons for your answer.