Question

Chapel Hill has decided to see if there is less drunk driving during the quarantine along a checkpoint on 15-501. It is known that before the quarantine the number of impaired drivers in an evening on 15-501 is normally distributed with mean of 73.5.

A) If the police department checks the data after quarantine for 7 evenings and gets the following results: 71, 66, 63, 72, 74, 70, 67.
What is the variance of this sample? _____
What is the value of our test statistic? _____
What is our p-value for the test? _____

B) Let's say we still don't know if drunk driving behavior has changed, but the Chapel Hill police department has been accused of "juking the stats" (inflating arrest numbers for nefarious reasons) so they've bought a new brand of breathalyzers so they can test every individual twice to make sure their drunk driving convictions stick. The police department wants to check if the blood alcohol content measurements for the new tests are different from the old tests. The first 12 measurements from breathalyzer 1 (multiplied by 10,000) are as follows:
4.4
2.1
3.6
9.2
7.3
7.9
8.4
1.2
0
11.4
5.5
3.6


The first 12 measurements from breathalyzer 2 (multiplied by 10,000) are as follows:
4.2
2.1
3
8.6
7.2
8.1
8.2
0.6
0.2
11.1
5.5
3.8

What is the value of the test statistic? (Give a positive value):______
What is the p-value for the test?:______

Answer 1

A) = (71 + 66 + 63 + 72 + 74 + 70 + 67)/7 = 69

Variance = ((71 - 69)^2 + (66 - 69)^2 + (63 - 69)^2 + (72 - 69)^2 + (74 - 69)^2 + (70 - 69)^2 + (67 - 69)^2)/6 = 14.6667

The test statistic is

  

P-value = P(T < -3.1088)

= 0.0104

B) = (0.2 + 0 + 0.6 + 0.6 + 0.1 + (-0.2) + 0.2 + 0.6 + (-0.2) + 0.3 + 0 + (-0.2))/12 = 0.1667

s_d = sqrt(((0.2 - 0.1667)^2 + (0 - 0.1667)^2 + (0.6 - 0.1667)^2 + (0.6 - 0.1667)^2 + (0.1 - 0.1667)^2 + (-0.2 - 0.1667)^2 + (0.2 - 0.1667)^2 + (0.6 - 0.1667)^2 + (-0.2 - 0.1667)^2 + (0.3 - 0.1667)^2 + (0 - 0.1667)^2 + (-0.2 - 0.1667)^2)/11) = 0.3085

The test statistic is

  

P-value = 2 * P(T > 1.8719)

= 2 * (1 - P(T < 1.8719))

= 2 * (1 - 0.9560)

= 0.0880