Question

For the following below you should decide

a) What test would you use?

b) Why would you use this test?

1. You want to know if major in university and tolerance of ambiguity are related. You choose 60 people (20 science majors, 20 humanities majors and 20 phys ed majors) and give them a test which measures their tolerance for ambiguity. You them separate them into low, moderate and high tolerance groups.

2. You wonder if the amount of time it takes a person to learn a new language is related to their age. You ask an instructor at an ESL (English as a second language) school to record the age of 40 new students and how long it took for them to become functionally literate.

3. You work for a manufacturer of fake finger nails. Your boss is interested in knowing if a new procedure can reduce the costs of making these nails. You randomly select the operating costs for 10 days at your plant and compare them to the cost for 10 days randomly selected from another plant that has switched to the new system. The old system had an average daily cost of $5400 with a variance of 120. The new system had an average daily cost of $5210 with a variance of 730.

Answer 1

1.) Here we can use the Chi-square test of independence. The reason we would use this test is that there are two factors here i.e tolerance groups and subject majors to which the student belongs.

Thus we can use the expected and observed frequency criteria to test the independence between the two attributes or to observe whether they are related if the null hypothesis is rejected.

2.) A Chi-square test for the goodness of fit can be used here. Here we can take the expected amount of time to be equal for all age students and then we observe the amount of time actually taken by each age group of students to learn the new language which can be recorded as observed frequency.

This can be used to examine if there is no significant difference between observed and expected frequency or whether the expected distribution is a good fit for the data.

3.) T test for the difference of means can be used here.

We can use the null hypothesis that the average of old system = average of new system vs the alternative hypothesis being that the average cost of the old system > average cost of the new system.

This comparison can help us examine if the cost is reduced by switching to the new system.