From past records it is known that the average life of a battery used in a digital clock is 305 days. The battery life is normally distributed. The battery was recently modified to last longer. A sample of 20 of the modified batteries was tested. It was discovered that the mean life was 311 days and the sample standard deviation was 12 days. We want to test at the 0.05 level of significance whether the modification increases the life of the battery. What is our decision rule?
A) Do not reject the null hypothesis if computed t is 1.96 or greater
B) Reject the null hypothesis if computed t is less than 1.96
C) Do not reject the null hypothesis if computed t is 1.729 or greater
D) Reject the null hypothesis if computed t is 2.086 or greater
E) Reject the null hypothesis if the computed t is 1.729 or greater

Question

Quizplus · Accepted Answer

Given the sample size (n=20) and the level of significance (0.05), we use a t-test to determine if the modification increases the battery life. The decision rule for a one-tailed t-test at the 0.05 significance level with 19 degrees of freedom (n-1) involves rejecting the null hypothesis if the computed t is greater than the critical t-value from t-distribution tables, which is approximately 1.729 for a one-tailed test.

From Past Records It Is Known That the Average Life