Two 95 percent confidence intervals will be constructed to estimate the difference in means of two populations, R and J. One confidence interval, I400, will be constructed using samples of size 400 from each of R and J, and the other confidence interval, I100, will be constructed using samples of size 100 from each of R and J.

When all other things remain the same, which of the following describes the relationship between the two confidence intervals?

a)The width of i400 will be 4 times the width of i100.
b) The width of i400 will be 2 times the width of i100
c)The width of i400 will be equal to the width of i100.
d)The width of I400 will be 1/2 times the width of I100
e)The width of I400 will be 1/4 times the width of I100.

e)The width of I400 will be 1/4 times the width of I100.

Step-by-step explanation:

If the confidence interval is 95% = 0.95, therefore α = 1 - 0.95 = 0.05.

The width of the confidence (W) is given by the equation:

,  where n is the sample size, is the standard deviation and is the z score of α/2

From the equation, we can see that the width is inversely proportional to the square root of the sample size.

Since nterval, I400, will be constructed using samples of size 400 from each of R and J, and the other confidence interval, I100, will be constructed using samples of size 100 from each of R and J. and  all other things remain the same.

Let be the width of I400 and be the width of I100. Therefore:

The width of I400 will be 1/4 times the width of I100.

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068