Question

a researcher wants to investigate whether there is a difference in the aerobic capacity between two different exercise programs. group 1 participates in a running program, and group 2 participates in a cycling program. after 8 weeks, the aerobic capacity is measured for both groups. below are the sample data:
group 1 (running program): sample size $(n_1)=3$, sample mean $(\overline{x}_1)=40$, sample variance $(s_1^2)=4$
group 2 (cycling program): sample size $(n_2)=4$, sample mean $(\overline{x}_2)=45$, sample variance $(s_2^2)=9$.
question 3:
what is the pooled variance?
4
6.5
7
9

Explanation:

Step1: Recall the formula for pooled variance

The formula for pooled variance \(s_p^2=\frac{(n_1 - 1)s_1^2+(n_2 - 1)s_2^2}{n_1 + n_2-2}\)

Step2: Substitute the given values

Given \(n_1 = 3\), \(s_1^2=4\), \(n_2 = 4\), \(s_2^2 = 9\)

First, calculate \((n_1 - 1)s_1^2=(3 - 1)\times4=2\times4 = 8\)

Second, calculate \((n_2 - 1)s_2^2=(4 - 1)\times9=3\times9 = 27\)

Then, \(n_1 + n_2-2=3 + 4-2=5\)

Now, \(s_p^2=\frac{8 + 27}{5}=\frac{35}{5}=7\)

Answer:

7