Question

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 -1.645 or to the right of 1.645B. ​To the left of -1.345 or to the right of 1.345C. ​To the left of -1.282 or to the right of 1.282D. ​Between -1.761 and 1.761

Answer 1

D. ​Between -1.761 and 1.761

Explanation:

T-table need to be used for the values of t to reject or not to reject the null hypothesis.

Since the sample size is 15, degrees of freedom is 15-1=14

Two tailed t-value at 0.10 significance level and 14 degrees of freedom is 1.761.

Therefore we fail to reject the null hypothesis for t-values between -1.761 and 1.761, since these values does not fall in the critical region.