Question

use 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 ≥ 7900; α = 0.10 sample statistics: ˉx = 7600, s = 440, n = 20
what are the null and alternative hypotheses?
a. h₀: μ ≠ 7900
hₐ: μ = 7900
b. h₀: μ ≤ 7900
hₐ: μ > 7900
c. h₀: μ = 7900
hₐ: μ ≠ 7900
d. h₀: μ ≥ 7900
hₐ: μ < 7900

Explanation:

Step1: Understand the claim

The claim is \(\mu\geq7900\). The null hypothesis \(H_0\) is the statement being tested and usually contains equality. The alternative hypothesis \(H_a\) is the statement we try to find evidence for.

Step2: Formulate \(H_0\) and \(H_a\)

Since the claim is \(\mu\geq7900\), the null hypothesis \(H_0:\mu\geq7900\) (the claim we assume to be true initially) and the alternative hypothesis \(H_a:\mu < 7900\) (the opposite of the claim for testing).

Answer:

D. \(H_0:\mu\geq7900\), \(H_a:\mu < 7900\)