Question

Examine the following hypothesis test with n = 16, s = 8, and x = 29.
H0
: μ ≥ 31
HA
: μ < 31
α = 0.10
a. State the decision rule in terms of the critical value of the test statistic.
b. State the calculated value of the test statistic.
c. State the conclusion.
a. State the decision rule. Select the correct choice below and fill in any answer boxes in your choice.
(Round to four decimal places as needed.)
A. Reject the null hypothesis if the calculated value of the test statistic, t, is greater than the
critical value of . Otherwise, do not reject.
B. Reject the null hypothesis if the calculated value of the test statistic, t, is less than the critical
value of or greater than the critical value of . Otherwise, do
not reject.
C. Reject the null hypothesis if the calculated value of the test statistic, t, is less than the critical
value of . Otherwise, do not reject.
b. State the calculated value of the test statistic.
t = (Round to three decimal places

Answer 1

Given the detail as:

Sample size n = 16, Sample standard deviation s = 8, and sample mean = 29.

Given the hypotheses are:

Ho: μ ≥ 31
H_A: μ < 31

and the level of significance as α = 0.10.

Based on the hypothesis it will be left tailed test, but since the population standard deviation is unknown hence t-distribution is applicable thus the degree of freedom will be used which is df = n-1= 16-1= 15.

a. The decision rule in terms of the critical value of the test statistic.

Rejection region:

The rejection region is calculated using the excel formula for t-distribution which is =T.INV(0.10, 15), thus the tc is computed as -1.3406.

C. Reject the null hypothesis if the calculated value of the test statistic, t, is less than the critical
value. Otherwise, do not reject.

b. Test statistic:

t = -1.000

c. Conclusion:

Since the test statistic is greater than tc hence we fail to reject the null hypothesis and conclude that there is insufficient to support the claim.