i) Compare the uses of the independent samples and paired samples t tests. Explain clearly in which circumstan

i) Compare the uses of the independent samples and paired samples t tests. Explain clearly in which circumstances each method should be used in preference to the other, illustrating your answer with appropriate examples. State briefly the appropriate assumptions made in each case. 

ii) In a particular population, it was of interest whether the male chief executive officer (CEO) was, on average, younger or older than their CEO female counterparts. A random sample of 15 firms was taken with the CEO age given in the table below. 

Firm No 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

Male, age 

39 

38 

73 

54 

24 

57 

49 

63 

48 

44 

26 

64 

42 

45 

61 

Female, age 

32 

31 

68 

58 

26 

53 

48 

69 

47 

46 

25 

62 

40 

48 

57 

(a) Use the above data to calculate the mean and standard deviation of the differences between the ages of the male managers and their female counterparts. (10% Mark) 

(b) Is there evidence that the mean difference in ages between male and female is non-zero? (5% Mark) 

(c) Obtain a 95% confidence interval for the mean difference in ages of the male and their female colleagues. (5% Mark)