Question

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.

Answer 1

Answer:

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 $\bar x _1 =$ 2.9

For women:

The sample size n₂ = 10

The standard deviation s₂ = 0.2

The sample mean $\bar x _2=$ 3.1

Using the pooled variance;

$S_i = \sqrt{\dfrac{s^2_1}{n_1} +\dfrac{s^2_2}{n_2} }$

$= \sqrt{\dfrac{0.2^2}{10} +\dfrac{0.2^2}{10} }$

$= \sqrt{0.004+0.004 }$

$= \sqrt{0.008 }$

= 0.08944

The z-test statistics is computed as:

$z = \dfrac{\barf x_1 - \bar x_2}{S_i}$

$z = \dfrac{2.9- 3.1}{0.08944}$

z = - 2.236

The p-value =  2 × P(Z < -2.236)

From the z table;

p-value = 2 × (0.012675)

p-value = 0.02535