I test the hypothesis H 0 : = 10 against H A : 10 . The sample mean is x = 8 and
ID: 3380977 • Letter: I
Question
I test the hypothesis H0: = 10 against HA: 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.
Explanation / Answer
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]