Question

For the following below you should decide

a) What test would you use?

b) Why would you use this test?

1. You think that the number of foreign cars on the road has changed over the last 10 years. You find out that in 1992 a sample of 100 people showed that 25 drove Japanese cars, 58 drove North American cars and 17 drove European cars. A sample collect this year had 31 driving Japanese cars, 51 driving North American cars and 18 driving European cars.

2. You think that Brock students are more active than other universities in terms of extracurricular activities. The average student at a Canadian university is involved in 3.5 extracurricular activities. The average Brock student is involved in 3.9 with a st dev of 2.1 activities.

3. You have three groups of students (biology majors, history majors and english majors). You think that these groups will differ on a measure of logical reasoning. You also have a theory that the type of school they go to may affect this measure so half of each group are from small primarily undergraduate universities and half are from large universities

Answer 1

1.

(a)

We shall perform Chi-square test.

(b)

To test whether there is significant difference between two distributions or not, we have to perform Chi-square test.

2.

(a)

We shall use t-test.

(b)

Here we are given with population mean but population standard deviation (or variance) is unknown to us (so z-test is not possible). We shall estimate population (Canadian university) standard deviation using given value of sample (Brock) standard deviation. So, we shall perform one tailed (right tailed) t-test.

3.

(a)

We shall perform two-way ANOVA.

(b)

In the given problem we have to compare among mean measures of logical reasoning of 3*2 = 6 groups (using analysis of variance). There is two way classification namely (i) subject wise (Biology majors, History majors and English majors) and (ii) type of universities (small primarily undergraduate universities and large universities).