Question

You have obtained the number of years of education from one random sample of 35 police officers from City A and the number of years of education from a second random sample of 30 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 2.2 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 z-test Chi-square test 2 sample paired t-test 2-sample t-test

Carry out the test. The test statistic =

and the p-value is =

There 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

(a)

Question:

What is the appropriate test for this case?

2-sample t-test

(b)

Question:

Carry out the test.

H0: Null Hypothesis: ( The education levels of police officers in City A and City B is not significantly different.)

HA: Alternative Hypothesis: ( The education levels of police officers in City A and City B is significantly different.) (Claim)

n1 = 35

1 = 15

s1 = 2

n2 = 30

2 = 14

s2 = 2.2

Pooled Standard Deviation is given by:

Test Statistic is given by:

So,

(i)

The test statistic = 1.919

(ii)

ndf = 35 + 30 -2 =63

By Technology, P Value = 0.0595

So,

the p-value is = 0.0595

(iii)

Since P - value = 0.0595 is greater than = 0.05, the difference is not significant. Fail to reject null hypothesis.

Correct option:

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.