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
what are the null and alternative hypotheses? choose the correct answer below.
a. h₀: μ ≥ 71
hₐ: μ < 71
b. h₀: μ ≠ 71
hₐ: μ = 71
c. h₀: μ ≤ 71
hₐ: μ > 71
d. h₀: μ = 71
hₐ: 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 = (round to three decimal places as needed.)

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\). Given \(n = 25\), so \(df=25-1=24\).

Step2: Use the t - distribution to find the P - value

We have a one - tailed (right - tailed) t - test with \(t = 0.45\) and \(df = 24\). Using technology (such as a TI - 84 Plus: tcdf(0.45,1E99,24)), we calculate the P - value.

Answer:

The P - value is \(0.329\)