Question

Suppose we take a sample of 18 men and 17 women to estimate the difference in average height between men and women. The men had an average height of 70 inches with a standard deviation of 3, and the women had an average height of 66 inches with a standard deviation of 2. Calculate the pooled sample variance (Sp^2) for a two-sample confidence interval for the difference in means.

Answer 1

`\S^2_p =((n_1-1)S^2_1 +(n_2 -1)S^2_2)/(n_1 +n_2 -2)`

And replacing we got:

`\S^2_p =((18-1)3^2 +(17 -1)2^2)/(18 +17 -2) = 6.576`

Explanation:

Data given

For this case we have the following info given:

`n_1 = 18` represent the random sample size of men

`n_2 = 17` represent the random sample size of women

`\bar X_1 = 70` represent the average for men

`\bar X_2 = 6` represent the average for women

`s_1 = 3` represent the sample deviation for men

`s_2 = 2` represent the sample deviation for women

Solution to the problem

The pooled variance is given by this formula:

`\S^2_p =((n_1-1)S^2_1 +(n_2 -1)S^2_2)/(n_1 +n_2 -2)`

And replacing we got:

`\S^2_p =((18-1)3^2 +(17 -1)2^2)/(18 +17 -2) = 6.576`

And the pooled sample deviation would be:

`S_p = 2.564`