A sample of 10 men's GPA in college has sample mean 2.9, and a sample of 10 women's GPA has sample mean 3.1. We also know the GPAs of men and women have the same standard deviation 0.2. Calculate the p value.

p-value = 0.02535

Step-by-step explanation:

From the information given:

For men:

The sample size n₁ = 10

The standard deviation s₁ = 0.2

The sample mean 2.9

For women:

The sample size n₂ = 10

The standard deviation s₂ = 0.2

The sample mean 3.1

Using the pooled variance;

= 0.08944

The z-test statistics is computed as:

z = - 2.236

The p-value =  2 × P(Z < -2.236)

From the z table;

p-value = 2 × (0.012675)

p-value = 0.02535