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

We need to calculate the test statistic to make a decision about whether to reject or fail to reject the null hypothesis. The test statistic is given by: z = (x̄ - μ) / (σ / sqrt(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. Plugging in the given values, we get: z = (21.431 - 22) / (1.295 / sqrt(100)) = -4.56 Using a significance level of α = 0.01, the critical z-value for a one-tailed test (since H_A: μ < 22 is the alternative hypothesis) is -2.33. Since our calculated test statistic (z = -4.56) is less than the critical z-value, we reject the null hypothesis in favor of the alternative. Therefore, we should reject H₀ and conclude that H_A is supported by the data. Hence, the correct answer is B)False.

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

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