Question

Given the hypotheses: H₀: μ = 590, H₁: μ ≠ 590, a random sample of 15 observations with a sample mean of 595 and sample standard deviation of 8. Using a 0.05 significance level, what is the decision rule?

a) Reject H₀ if z > 1.96 or z < -1.96
b) Reject H₀ if z > 1.64 or z < -1.64
c) Reject H₀ if z > 1.28 or z < -1.28
d) Reject H₀ if z > 1.05 or z < -1.05

Answer 1

The decision rule for the given hypothesis test is to reject H₀ if z > 1.96 or z < -1.96.

Step-by-step explanation:

To determine the decision rule for this hypothesis test, we need to find the critical z-values for a significance level of 0.05. Since it is a two-tailed test (H₁: μ ≠ 590), we divide the significance level by 2 to get 0.025 for each tail. Looking up this value in the standard normal distribution table, we find that the critical z-values are approximately -1.96 and 1.96. Therefore, the correct decision rule is a) Reject H₀ if z > 1.96 or z < -1.96.