Stataistic

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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