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)
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