The null and alternate hypotheses are:
The following paired observations show the number of traffic citations given for speeding by Officer Dhondt and Officer Meredith of the South Carolina Highway Patrol for the last five months.
| Day | ||||
May | June | July | August | September | |
Officer Dhondt | 30 | 22 | 25 | 19 | 26 |
Officer Meredith | 26 | 19 | 20 | 15 | 19 |
At the .05 significance level, is there a difference in the mean number of citations given by the two officers?
Note: Use the five-step hypothesis testing procedure to solve the following exercises.
Denote the traffic citations given by Officer Dhondt as the first population and those given by Officer Meredith as the second population. Using the table of the t-distribution with degrees of freedom for a two-tailed test we find that the value of t for the probability 0.05 is 2.776. We will reject the null hypothesis if the value of the test statistic is less than or more than 2.776.
The differences are 4, 3, 5, 4, and 7. The sample mean and standard deviation are
The test statistic is
Since, we reject the null hypothesis. There is evidence that the population means are different.