Exercise 8.2: Statistical Inference

Exercise 8.2

1.   Mention two branches of statistical inference?

2.   What is an estimator?

3.   What is an estimate?

4.   What is point estimation?

5. What is interval estimation?

6. What is confidence interval?

7. What is null hypothesis? Give an example.

8. Define alternative hypothesis.

9. Define critical region.

10. Define critical value.

11.  Define level of significance

12. What is type I error

13. What is single tailed test.

14. A sample of 100 items, draw from a universe with mean value 4 and S.D 3, has a mean value 63.5. Is the difference in the mean significant?

15. A sample of 400 individuals is found to have a mean height of 67.47 inches. Can it be reasonably regarded as a sample from a large population with mean height of 67.39 inches and standard deviation 1.30 inches?

16. The average score on a nationally administered aptitude test was 76 and the corresponding standard deviation was 8. In order to evaluate a state’s education system, the scores of 100 of the state’s students were randomly selected. These students had an average score of 72. Test at a significance level of 0.05 if there is a significant difference between the state scores and the national scores.

17. The mean breaking strength of cables supplied by a manufacturer is 1,800 with a standard deviation 100. By a new technique in the manufacturing process it is claimed that the breaking strength of the cables has increased. In order to test this claim a sample of 50 cables is tested. It is found that the mean breaking strength is 1,850. Can you support the claim at 0.01 level of significance.

Answers:

14. |z| = 1.667 

15. 1.2308 

16. |z| = 5 

17. 3.536