Question

Tom Sevits is the owner of the Appliance Patch. Recently, Tom observed a difference in the dollar value of sales between students and non-students he employs as sales representatives. A sample of 40 days revealed the non-students sold a mean of $1400 worth of appliances per day. For a sample of 50 days, the students sold a mean of $1500 worth of appliances per day. Assume that the population standard deviation for non-students is $200 and for students is $250. At the 0.05 significance level, can Mr. Sevits conclude that the mean amount sold per day is larger for the students?

Answer 1

Using a two-sample z-test, we can determine whether there is a significant difference between the mean sales of non-students and students. The test compares the sample means, sample sizes, and known standard deviations against a 0.05 significance level to decide whether to reject the null hypothesis.

Step-by-step explanation:

To determine whether Tom Sevits can conclude that the mean amount sold per day is larger for the students than for the non-students, we need to perform a two-sample z-test since the population standard deviations are known. The hypothesis for our test is set up as follows:

• Null Hypothesis (H0): μnon-students ≥ μstudents
• Alternative Hypothesis (H1): μnon-students < μstudents

We'll use the 0.05 significance level for our test. To conduct the test, we calculate the z-statistic using the provided sample means, sample sizes, and population standard deviations. When we calculate the z-statistic and compare it with the critical z-value corresponding to the 0.05 significance level in the z-distribution table, we can make a decision about the hypothesis based on whether the z-statistic falls in the rejection region or not.