Question

use the following information to complete steps (a) through (d) below. a random sample of size ( n_1 = 31 ) results in a sample mean of 124.3 and a sample standard deviation of 8.5. an independent sample of size ( n_2 = 50 ) results in a sample mean of 131.8 and sample standard deviation of 7.3. does this constitute sufficient evidence to conclude that the population means differ at the ( alpha = 0.10 ) level of significance? (a) what type of test should be used? a. a hypothesis test regarding two population standard deviations. b. a hypothesis test regarding the difference of two means using welchs approximate t. c. a hypothesis test regarding the difference between two population proportions from independent samples. d. a hypothesis test regarding the difference of two means using a matched - pairs design.

Explanation:

• Option A: Incorrect. The problem is about means, not standard deviations.
• Option B: Incorrect. Welch's \(t\) - test is used for difference in means when population variances are unknown and not assumed equal (which is the case here as we have two independent samples with different sample sizes and sample standard deviations).
• Option C: Correct. We have two independent samples (\(n_1 = 31\), \(n_2=50\)), sample means (\(\bar{x}_1 = 124.3\), \(\bar{x}_2 = 131.8\)), sample standard deviations (\(s_1 = 8.5\), \(s_2=7.3\)). Since the population variances are unknown and we do not assume them to be equal, a hypothesis test regarding the difference of two means using Welch's approximate \(t\) is appropriate.
• Option D: Incorrect. A matched - pairs design is for dependent samples (e.g., before - after measurements on the same subjects), but here the samples are independent.

Answer:

C. A hypothesis test regarding the difference of two means using Welch's approximate \(t\)