We are testing H₀: μ ≥ 22;versus H_A: μ

Question

We are testing H₀: μ ≥ 22;versus H_A: μ < 22.Given α = .01,n = 100, = 21.431,and σ = 1.295,we should not reject H₀.

Quizplus · Accepted Answer

To conduct a one-tailed test, we need to compute the test statistic using the formula: z = (x̄ - μ) / (σ / √n) where x̄ is the sample mean, μ is the hypothesized population mean, σ is the population standard deviation, and n is the sample size. Using the given values, we have: z = (21.431 - 22) / (1.295 / √100) = -2.684 Since we are testing the hypothesis that μ < 22, we need to find the area under the standard normal distribution curve to the left of z = -2.684. Using a standard normal table or calculator, we find this area to be approximately 0.0036. Since α = 0.01, which is greater than 0.0036, we can reject the null hypothesis H₀ and conclude that the population mean is less than 22. Therefore, the correct answer is B.

We Are Testing H0: μ ≥ 22;versus HA: μ

We Are Testing H₀: μ ≥ 22;versus H_A: μ