In: Economics
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?
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