Question

You have obtained the number of years of education from one random sample of 38 police officers from City A and the number of years of education from a second random sample of 40 police officers from City B. The average years of education for the sample from City A is 15 years with a standard deviation of 2 years. The average years of education for the sample from City B is 14 years with a standard deviation of 2.8 years. Is there a statistically significant difference between the education levels of police officers in City A and City B?

What is the appropriate test for this case?

2-sample t-test2 sample paired t-test     2 sample z-testChi-square test

Carry out the test. The test statistic =   (round answer to two decimal places.)
and the p-value is= (round answer to 2 decimal places)

There  --- is not is sufficient evidence at the 5% level to conclude that the education levels of police officers in City A and City B is significantly different.

Answer 1

Solution:

What is the appropriate test for this case?

Answer: 2-sample t-test because we have two independent groups under study and the population standard deviations are unknown

We can use the TI-84 to find the test statistic and the p-value. The steps are as follows:

Press STAT and then scroll right to TESTS.

Scroll down to 2-SampTTest and scroll right to Stats

Enter the values as:

Press Calculate and the output is:

The test statistic = 1.82
and the p-value is= 0.07

There is not sufficient evidence at the 5% level to conclude that the education levels of police officers in City A and City B is significantly different.