Question

Indices   DUR   DUR (OLD)
1   6   11
2   13   14
3   11   14
4   7   10
5   9   9
6   7   10
7   8   11
8   5   8
9   7   6
10   7   10
11   7   13
12   3   5
13   10   13
14   3   15
15   4   12
16   9   7
17   9   8
18   10   13
19   6   10
20   8   14
21   10   14
22   8   18
23   2   10
24   4   11
25   7   16
26   10   9
27   11   20
28   7   8
29   11   9
30   13   12
31   12   12
32   11   10
33   7   12
34   9   12
35   5   11
36   9   15
37   4   18
38   8   12
39   13   9
40   8   10
41   13   11
42   16   11
43   7   16
44   10   11
45   15   10
46   10   12
47   19   19
48   15   12
49   12   12
50   11   10
51   13   8
52   9   8
53   6   11
54   6   21
55   12   12
56   11   14
57   13   14
58   13   20
59   10   10
60   8   10
61   14   10
62   10   10
63   18   9
64   8   15
65   9   12
66   8   13
67   8   7
68   8   8
69   13   8
70   12   10
71   12   9
72   14   10
73   8   14
74   9   8
75   14   12
76   7   13
77   8   10
78   9   11
79   10   15
80   10   9
81   16   20
82   17   9
83   10   11
84   6   19
85   19   16
86   17   14
87   8   17
88   7   10
89   3   15
90   12   13
91   6   15
92   10   12
93   16   12
94   14   10
95   11   16
96   9   10
97   11   10
98   12   10
99   19   14
100   13   17
101   9   12
102   24   12
103   9   12
104   9   10
105   5   22
106   9   16
107   8   10
108   9   7
109   10   12
110   17   13
111   7   16
112   9   22
113   4   9
114   13   10
115   21   11
116   10   9
117   11   13
118   8   12
119   10   9
120   9   14
The same exact responders were interviewed again the next day, at the same exact times, by researchers of a different company. The duration of the interview in minutes for each responder, for this new survey, is given . Using a 95% confidence interval, would you say that the interviews contacted by this new company were more efficient than the ones contacted by the first company the day before, in terms of the duration of the interview in minutes, on average?

Answer 1

From the data,

mean difference of DUR (OLD) - DUR = m = 2.033333

Standard deviation of the difference DUR (OLD) - DUR = s = 5.130127

Degree of freedom = n - 1 = 120 - 1 = 119

t value for df = 119 and 95% confidence interval is 1.98

Standard error of mean difference, se = s / = 5.130127 / = 0.4683144

Margin of error = t * se = 1.98 * 0.4683144 = 0.9272625

95% confidence interval of mean difference in duration of the interview is,

(2.033333 - 0.9272625, 2.033333 + 0.9272625)

(1.10607, 2.960595)

As, 95% confidence interval of mean difference in duration of the interview does not contain the value 0, we can conclude that the interviews contacted by this new company were more efficient than the ones contacted by the first company the day before.