For each of the following scenarios, which of the following hypothesis tests is

Question

For each of the following scenarios, which of the following hypothesis tests is most appropriate: one sample proportion, one sample mean, two independent proportions, two independent means, or two paired (dependent) means? Explain why.

1.) Bradford's College of Education wants to know if applicants to their M.Ed. programs and their M.S. programs differ in terms of whether or not they have work experience.

2.) The manager of a retail store wants to know if the average age of customers in her store is greater than 35 years.

3.) Bradford's Department of Statistics wants to know if applicants to its major have SAT-Math scores that are higher than their SAT-Verbal scores. They take a simple random sample of 40 applicants and record each individual’s SAT-Math and SAT-Verbal scores.

Explanation / Answer

1) Here we have to test whether proportion of applicants of M.Ed program who have work experience and proportion of applicants of M.S. programs who have work experience differ or not. So we have two independent proportions in this case and we have test their equality. Hence it is a test of two independent proportions. (Ans).

2) In this case the manager should take a random sample from her customers and note their ages. Then she should test whether the average age of the customers is greater than 35 years or not. So it is a test of one-sample mean. (Ans).

3) Here for each of the 40 applicants we have to record the SAT-Math scores and SAT-Verbal scores. Then we have to compare those scores pairwise in order to test whether SAT-Math scores are higher than SAT-Verbal scores. Hence it is a test of two-paired (dependent) means. (Ans).

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