Question

A test is made of H₀: μ = 68 versus H₁: μ≠68. A sample of size n=60 is drawn, and x = 73 The population standard deviation is σ = 23. Compute the value of the test statistic z and determine if H₀ is rejected at the σ = 0.05 level.

Answer 1

The test statistic z for the hypothesis test is approximately 1.645, which is less than the critical z-value for α = 0.05 in a two-tailed test (±1.96), so we do not reject the null hypothesis H0: μ = 68 at the 0.05 level.

Step-by-step explanation:

In the scenario described, you are performing a hypothesis test for a single population mean (μ) using a normal distribution, which is often referred to as a z-test. The test statistic z can be calculated using the formula:

z = (x - μ) / (σ / √n)

Given μ0 (the null hypothesis mean) = 68, the sample mean x = 73, population standard deviation σ = 23, and sample size n = 60, plug these values into the formula to get:

z = (73 - 68) / (23 / √60) = 5 / (23 / 7.746) ≈ 1.645

With this test statistic z, you can compare it to the critical z-value for a significance level (α) of 0.05 in a two-tailed test. The critical z-values for a significance level of 0.05 are approximately ±1.96. Since the calculated z-value (1.645) is less than 1.96, you do not reject the null hypothesis H0: μ = 68 at the 0.05 significance level.