Question

A random sample of size 20 is selected from a normal population for which the population standard deviation is unknown. Assume the null hypothesis indicates a two-tailed test and the researcher decides to use the 0.01 significance level. What values of t will cause the researcher to not reject the null hypothesis?

Group of answer choices

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 -2.861 and 2.861

D To the left of -1.645 or to the right of 1.645

Answer 1

The values of t that will cause the researcher to not reject the null hypothesis are between -2.861 and 2.861.

Step-by-step explanation:

In this case, the researcher is conducting a two-tailed test with a 0.01 significance level (alpha = 0.01). The critical values for a two-tailed test with 20 degrees of freedom can be found using the t-distribution table. These critical values correspond to the values of t that will cause the researcher to not reject the null hypothesis.

The critical t-values for a two-tailed test with alpha = 0.01 and 20 degrees of freedom are -2.861 and 2.861. Therefore, if the calculated t-value falls within this range, the researcher will not reject the null hypothesis.

Therefore, the correct answer is: C. Between -2.861 and 2.861.