Question

For each of the following you should decide
a) What test would you use?
b) Why would you use this test?

1. You wonder if changing the format on a statistics test will change the average mark on the test. You randomly select half the class and give them the standard test. The other half receives the test with the new format. You then compare the marks for each half. In analyzing the data you notice that the group that got the standard test has a normal distribution but the new format has created a bimodal distribution in that half of the class.

2. You wonder which gas station has better service Petro Canada or Shell. Over a 10 day period you ask 30 people to visit the Petro Canada and the Shell station. Each person purchases exactly $10 worth of gas at one station then drives across the road and gets $10 at the other station. You then record the time it takes for each person to be served.

3. You want to see if Rec and Leisure students get summer jobs faster than other university students. You find out from the student placement service that the average university student gets a summer job in 4 weeks with a variance of 3 weeks. The average Rec and Leisure student gets a job in 3.6 weeks with a variance of 4.2 weeks.

Answer 1

1.) a.) Here we can use the t-test for the difference of means

b.) The reason we use this test here is that the two group averages i.e. the one with standard test and the other with new format need to be compared with respect to their average marks in order to determine whether the change in format will also change their scores. So we use the null hypothesis that the average marks for both the groups are the same vs the alternative hypothesis that the average marks are different for both the groups.

2.) a.) Here also we can use the t-test for the difference of means.

b.) Here, the mean time taken to serve each of the 30 people will be recorded for both the shell station and petro Canada station separately. The null hypothesis will be that the average time is the same for the service at both stations and the alternative hypothesis will be that both the averages are not the same. If the null hypothesis is rejected then we can compute the standard deviation for service time of both the stations and the one with a smaller standard deviation can be concluded as a better service station.

3.) a.) T-test for the difference of means with a left-tailed alternative hypothesis.

The average time for university students to get a job will be compared with the average time for rec and leisure students to get the job.

For this comparison, the null hypothesis would be that the population mean time taken for the rec and leisure students is same as that of the university students and the alternative hypothesis is that the population mean time taken for the rec and leisure students < population mean time taken by the university students to get the job.

The sample means known for both the groups would be used in the computations of the test statistic for this test.

If we reject the null, we conclude that yes the Rec and Leisure students get summer jobs faster than other university students.