Question

The medical school of Wisconsin conducted an investigation to determine whether women and men complete medical school in significantly different amounts of time, on average. Two independent random samples were selected. State the appropriate null and alternative hypotheses. Perform the appropriate test of hypothesis to determine whether there is a significant difference in time to completion of medical school between women and men. Test using α = 0.05. You find the p-value associated with the test in the second question as 0.2224; explain how to use it for testing the hypothesis in the first question.

A) Null: μ₁ = μ₂, Alternative: μ₁ ≠ μ₂
B) Null: μ₁ = μ₂, Alternative: μ₁ < μ₂
C) Null: μ₁ = μ₂, Alternative: μ₁ > μ₂
D) Null: μ₁ ≠ μ₂, Alternative: μ₁ = μ₂

Answer 1

The correct hypotheses are the two-tailed A) Null: μ₁ = μ₂, Alternative: μ₁ ≠ μ₂. Given a p-value of 0.2224 and alpha of 0.05, we do not reject the null hypothesis as the p-value is greater than the alpha level.

Step-by-step explanation:

The appropriate null and alternative hypotheses for investigating whether there is a significant difference in the time to completion of medical school between women and men are A) Null: μ₁ = μ₂, Alternative: μ₁ ≠ μ₂. This represents a two-tailed test where you are looking for any significant difference, whether men complete medical school faster than women, or vice versa.

Given the p-value of 0.2224 and the significance level α = 0.05, you compare the p-value to the alpha. Since the p-value (0.2224) is greater than the alpha (0.05), you do not reject the null hypothesis. This means that there is not enough statistical evidence at the 5 percent significance level to conclude that a significant difference exists in the average time to complete medical school between women and men.