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

To calculate the p-value, use a two-sample t-test to compare the mean GPAs of the two groups. Calculate the pooled standard deviation and the t-value, then use the t-distribution to determine the p-value.

Step-by-step explanation:

The p-value provides evidence to support or reject a null hypothesis. In this case, we want to compare the mean GPA of men to women. The null hypothesis assumes that there is no difference between the means of the two groups, while the alternative hypothesis assumes that there is a difference.

To calculate the p-value, we can use a two-sample t-test since we have two independent samples. We will compare the means of the two groups using the sample means and standard deviations.

1. Calculate the pooled standard deviation using the formula:

• pooled standard deviation = sqrt(((n1-1) * s1^2 + (n2-1) * s2^2) / (n1 + n2 - 2))

Calculate the t-value using the formula:

• t = (mean1 - mean2) / (pooled standard deviation * sqrt(1/n1 + 1/n2))

Finally, calculate the p-value using the t-distribution with the degrees of freedom equal to (n1 + n2 - 2), where n1 and n2 are the sample sizes of men and women respectively.

Answer 2

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{(s^2_1)/(n_1) +(s^2_2)/(n_2) }`

`= \sqrt{(0.2^2)/(10) +(0.2^2)/(10) }`

`= √(0.004+0.004 )`

`= √(0.008 )`

= 0.08944

The z-test statistics is computed as:

`z = (\barf x_1 - \bar x_2)/(S_i)`

`z = (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