I test the hypothesis H0 10 against HA 10 The sample mean i

I test the hypothesis H₀: = 10 against H_A: 10. The sample mean is x = 8 and the corresponding t-value for the test is -2. As the sample size is 20, use the t-distribution with 19 degrees of freedom to determine the result of the test at the 5% significance level.

A) The p-value is between 95-97.5%, hence there is evidence to suggest that the alternative, < 10, is true.

B)The p-value is between 2.5-5%, hence there is NO evidence to suggest that the alternative is true.    

C) The p-value is between 5-10\\%, hence there is no evidence to suggest that the alternative, 10, is true.

D) The p-value is between 2.5-5%, hence there is evidence to suggest that the alternative, < 10, is true.

Please show the work and not just the final answer by itself.

Solution

Using a table, if df = 19, then we see that a two tailed P value for t = -2 is between 0.05 and 0.10, which is greater than 0.05, so we fail to reject Ho.

Thus,

OPTION C: The p-value is between 5-10%, hence there is no evidence to suggest that the alternative, 10, is true. [ANSWER, C]