Question

use technology and a t - test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. assume the population is normally distributed.
claim: μ > 71; α = 0.01 sample statistics: ˉx = 71.3, s = 3.3, n = 25
h_a: μ < 71
h_a: μ = 71
c. h_0: μ ≤ 71
h_a: μ > 71
d. h_0: μ = 71
h_a: μ ≠ 71
what is the value of the standardized test statistic?
the standardized test statistic is 0.45. (round to two decimal places as needed.)
what is the p - value of the test statistic?
p - value = 0.329 (round to three decimal places as needed.)
decide whether to reject or fall to reject the null hypothesis. choose the correct answer below.
a. reject h_0. there is enough evidence to support the claim.
b. reject h_0. there is not enough evidence to support the claim.
c. fall to reject h_0. there is not enough evidence to support the claim.
d. fall to reject h_0. there is enough evidence to support the claim.

Explanation:

Step1: Recall the decision rule for hypothesis testing

If \(P - value\geq\alpha\), we fail to reject the null hypothesis \(H_0\). If \(P - value<\alpha\), we reject the null hypothesis \(H_0\).

Step2: Compare the P - value and \(\alpha\)

We are given that \(\alpha = 0.01\) and \(P - value=0.329\). Since \(0.329\geq0.01\) (i.e., \(P - value\geq\alpha\)).

Answer:

C. Fall to reject \(H_0\). There is not enough evidence to support the claim.