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 4:
what is the degrees of freedom for this test?
○ 4
○ 5
○ 6
○ 7

Explanation:

Step1: Determine the formula for degrees of freedom

For an independent - samples t - test (assuming equal variances), the formula for degrees of freedom is \(df=n_1 + n_2-2\).

Step2: Substitute the values of \(n_1\) and \(n_2\)

Given \(n_1 = 3\) and \(n_2=4\), we substitute into the formula: \(df=3 + 4-2\).

Step3: Calculate the degrees of freedom

\(df=3 + 4-2=5\)

Answer:

5