A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume the null hypothesis indicates a two-tailed test and the researcher decided to use the 0.10 significance level. For what values of t will the null hypothesis not be rejected?
A)To the left of −1.282 or to the right of 1.282
B)To the left of −1.345 or to the right of 1.345
C)Between −1.761 and 1.761
D)To the left of −1.645 or to the right of 1.645

Question

Quizplus · Accepted Answer

Since the population standard deviation is unknown and the sample size is less than 30, a t-distribution is used. For a two-tailed test with a significance level of 0.10 and 14 degrees of freedom (n-1 = 15-1), the critical t-values are approximately ±1.761, meaning the null hypothesis will not be rejected for t-values between -1.761 and 1.761.

A Random Sample of Size 15 Is Selected from a Normal