Problem

The null and alternate hypotheses are:  The following paired observations show the number...

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.

Step-by-Step Solution

Solution 1

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.

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