Question

Determine whether to reject or fail to reject H₀ at the level of significance of​ a) α = 0.04 and​ b) α = 0.02.

H₀​: µ = 148​, Ha​: µ ≠148​, and P = 0.0209.​

A) Do you reject or fail to reject H₀ at the 0.04 level of​ significance?
B) Do you reject or fail to reject H₀ at the 0.02 level of​ significance?

Answer 1

At α = 0.04, we reject the null hypothesis because the p-value is smaller. However, at α = 0.02, we fail to reject the null hypothesis since the p-value is marginally greater.

Step-by-step explanation:

To determine whether to reject or fail to reject the null hypothesis H0: μ = 148, we will compare the p-value with our level of significance α. Given that the p-value is 0.0209:

• a) α = 0.04: Since the p-value (0.0209) is less than the level of significance (α = 0.04), we reject H0.
• b) α = 0.02: Since the p-value (0.0209) is slightly greater than the level of significance (α = 0.02), we fail to reject H0.

Thus, our decision will change depending on the selected level of significance, demonstrating the importance of context and predefined criteria for hypothesis testing.