Exercises on t-tests and confidence intervals

 Here are tables of the standard normal, student t, Fisher F and chi-square distributions.

Exercise 1

In a study one group of test animals was given a certain soft steroid, while another group was given no such steroids. After a period the increase in weight (in grams) was measured, and gave the results reported in the table:

 

Treatment	Sample size	Sample mean	Sample standard deviation
Steriod	8	32.8	2.6
Control	10	40.5	2.5

 

Find a 90 % confidence interval for the difference in weight increase for the two groups.

 

 

 

Exercise 2

In a study a group of men was given calcium supplement for 12 weeks, while a control group got no such supplement. The reduction in systolic blood pressure was measured and gave the result reported in the table:

 

Treatment	Sample size	Sample mean	Sample standard deviation
Calcium group	10	5.00	8.74
Control group	11	-0.27	5.90

 

Perform a t-test to decide whether the intake of calcium reduces the systolic blood pressure.

 

 

Exercise 3

In a study the strength of seven fabrics was tested in both an unabraded condition and in an abraded condition. The following breaking loads (in kg/25 mm width) were recorded:

 

	1	2	3	4	5	6	7
Unabraded	36.4	51.5	38.7	43.2	48.8	25.6	49.8
Abraded	28.5	46.0	34.5	36.5	52.5	26.5	46.5
Difference	7.9	5.5	4.2	6.7	-3.7	-0.9	3.3

 

One is interested in studying the reduction in strength by abrading the fabrics.

 

a) Explain why it is not appropriate to consider this as a two-sample problem.

 

To perform an appropriate analysis, one may compute the difference in strength for each of the seven fabrics, and the use methods for one sample based on these differences. (The mean difference is 3.29 and the standard deviation of the differences is 4.18.)

 

b) Compute a 95 % confidence interval for the reduction in strength using this approach.