Question

Mean hours studied by two independent groups of students are displayed below:

Sample I: Student athletes n₁ = 65; sample mean (xı-bar) = 20.6; S₁ = 5.25
Sample II: Student non-athletes n₂ = 175; sample mean (x₂-bar) = 23.5; S₂ = 3.85
(a) Do these samples provide sufficient evidence to conclude that the population mean hours of non-athletes and athletes differ? Use α=0.10.

Answer 1

To investigate whether the mean study hours of athletes and non-athletes differ, a two-sample t-test should be performed. The null hypothesis asserts no difference between the group means, while the alternative hypothesis suggests a difference. The test involves calculating a t-statistic and comparing it to a critical value at a 0.10 significance level.

Step-by-step explanation:

To determine if there is sufficient evidence to conclude that the population mean hours of non-athletes and athletes differ, we should perform a two-sample t-test (independent samples).

Step-by-Step Procedure

1. State the null hypothesis (H0): μ1 = μ2 (the population means are equal).
2. State the alternative hypothesis (H1): μ1 ≠ μ2 (the population means are not equal).
3. Choose the significance level, α = 0.10.
4. Calculate the degrees of freedom and the critical t-value for the t-test.
5. Compute the test statistic using the formula for the t-test for two independent samples.
6. Compare the calculated t-statistic with the critical t-value to determine if the difference is statistically significant.

Using the given sample sizes (⅓ = 65, ⅔ = 175), sample means (x₁-bar = 20.6, x₂-bar = 23.5), and standard deviations (S₁ = 5.25, S₂ = 3.85), we can calculate the t-statistic. If the absolute value of the t-statistic is greater than the critical t-value, we reject the null hypothesis in favor of the alternative hypothesis, concluding that there is a significant difference between the mean hours studied by athletes and non-athletes.