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:

Since we are comparing the means of two independent samples (with different sample sizes \(n_1 = 31\) and \(n_2=50\), different sample standard deviations \(s_1 = 8.5\) and \(s_2 = 7.3\)), and we do not assume that the population variances are equal, Welch's approximate \(t\) - test for the difference of two means is appropriate. A matched - pairs design would require paired data (not the case here). Testing population standard deviations (Option A) or population proportions (Option C) is not relevant as the problem is about means.

Answer:

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