2. A researcher collects data on two independent samples. The first group consists of 20 human subjects, has a sample mean of 4.21, and a standard deviation of 1.4. The second group consists of 20 subjects, has a sample mean of 3.15, and a standard deviation of 1.8. Test the null hypothesis that there is no difference between the population means of the two groups at the .01 level of significance. Indicate a) the observed value of the test statistic, b) the critical value(s), c) whether you reject or fail to reject the null hypothesis.

3. A researcher collects data on two independent samples. The first group consists of 20 human subjects, has a sample mean of 4, and a variance of 5. The second group consists of 10 subjects, has a sample mean of 6, and a variance of 9. Test the null hypothesis that there is no difference between the population means of the two groups at the .10 level of significance. Indicate a) the observed value of the test statistic, b) the critical value(s), c) whether you reject or fail to reject the null hypothesis.

4. A shoe company wants to compare two materials (A and B) for use on the soles of boys’ shoes. Now, you would expect certain variability among boys- some boys wear out shoes much faster than others. A problem arises if this variability is large. It might completely hide an important difference between the two materials. Suppose we give each boy a special pair of shoes with the sole on one shoe made from material A and the other from material B. This procedure produced the data in the table below: (the measured dat represents the height of the sole in millimeters) Is there enough evidence to show that Material B is better than Material A?

Boy COLUMN 1

1

2

3

4

5

6

7

8

9

10

Material A COLUMN 2

13.2

8.2

10.9

14.3

10.7

6.6

9.5

10.8

8.8

13.3

Material B Column 3

14.0

8.8

11.2

14.2

11.8

6.4

9.8

11.3

9.3

13.6