Question

You collect the following data on the average speed (in miles per hour) of a student driver on the highway:

Speed
68
66
69
82
83
82
75
79
86
79
80
79
77
59
73
72
71
51
73
100
73
80
80
67
72
70
67
68
75
66
63
87
72
62
69
58
74
78
73
67
73
79
84
75
65
65
68
78
64
60
85
77
82
86
74
87
100
77
71
75
72
72
76
58
76
63
76
72
66
73
79
83
84
86
78
78
77
64
65
78
68
81
92
86
56
84
83

a.If you want to construct a 95% confidence interval, what would use for the t-critical value?

b. what would be the lower boundof your 95% confidence interval?

c. what would be the upper bound of your 95% confidence interval?

Answer 1

a) To construct a 95% confidence interval, we will use the critical value of t as 1.96. We will use the two-tailed value for this purpose, and given that we have 87 variables, the value with 86 (87 - 1) degrees of freedom. The corresponding value is found to be 1.96.

To create the confidence interval, we will use the following formula.

From the data set above, we can calculate the mean by summing the observations and dividing by the number of observations. This comes out to 74.43. Similarly, we can calculate our sample standard deviation by taking the sum of squared deviations and dividing by 86, i.e. n-1. We get our sampe standard deviation 's' as 9.05. Hence we have all our parameters:

Xmean = 74.43

t = 1.96

s = 9.05

n = 87

We can now calculate the confidence interval using the formula above. This comes out to be,

74.43 +/- 1.90

b) Therefore, the lower bound of the confidence interval is 74.43 - 1.90 = 72.53

c) Therefore, the upper bound of the confidence interval is 74.43 + 1.90 = 76.33