Question

state your conclusion to the hypothesis test.
if a 95% confidence interval for μ is calculated to be (21.4, 27.9), what would be the result of a hypothesis test at a 5% significance level performed on the following set of hypotheses?
h₀: μ = 27 vs hₐ: μ ≠ 27
there is not enough information to test this hypothesis
the null hypothesis would be rejected
the alternative hypothesis would be rejected
the null hypothesis would not be rejected

Explanation:

Step1: Understand the relationship between confidence interval and hypothesis test

A 95% confidence interval is related to a hypothesis test at the 5% significance level. If the hypothesized value lies within the confidence interval, we fail to reject the null hypothesis. If it lies outside, we reject the null hypothesis.

Step2: Check if the hypothesized value \( \mu = 27 \) is in the confidence interval \((21.4, 27.9)\)

The value \( 27 \) is within the interval \((21.4, 27.9)\)

Answer:

The null hypothesis would not be rejected.