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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.

Respuesta :

Answer:

[tex]\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}[/tex]

And replacing we got:

[tex]\S^2_p =\frac{(18-1)3^2 +(17 -1)2^2}{18 +17 -2} = 6.576[/tex]

Step-by-step explanation:

Data given

For this case we have the following info given:

[tex]n_1 = 18[/tex] represent the random sample size of men

[tex]n_2 = 17[/tex] represent the random sample size of women

[tex]\bar X_1 = 70[/tex] represent the average for men

[tex]\bar X_2 = 6[/tex] represent the average for women

[tex]s_1 = 3[/tex] represent the sample deviation for men

[tex]s_2 = 2[/tex] represent the sample deviation for women

Solution to the problem

The pooled variance is given by this formula:

[tex]\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}[/tex]

And replacing we got:

[tex]\S^2_p =\frac{(18-1)3^2 +(17 -1)2^2}{18 +17 -2} = 6.576[/tex]

And the pooled sample deviation would be:

[tex] S_p = 2.564[/tex]

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