Question

 

Statistics in Psychological Research

 

The average age for licensed drivers in a county is m = 42.6, s = 12 and the distribution is approximately normal. A county police officer was interested in whether the average age of those receiving parking tickets differed from that of the average age of the population. She obtained a sample of drivers receiving parking tickets. The ages for these drivers are listed below.

Perform the six steps of hypothesis testing necessary to determine whether this group differs from the population of drivers in the county. Use α = .05 Be sure to write out each step and show your work along the way. [20 points total]

Driver ages

41

37

17

59

22

69

48

19

Answer 1

Step 1: Hypothesis

Ho: = 42.6

Ha: 42.6

Null hypothesis states that the average age of those receiving parking tickets is same as the average age of licensed drivers in a county (i.e. population of drivers.)

Alternative hypothesis states that that the average age of those receiving parking tickets is not same as the average age of licensed drivers in a county (i.e. population of drivers.)

Step 2 : Significance level

Level of significance for the test = 0.05.

Step 3: Test statistics

n = 8

sample mean = sum of all terms / no of terms = 312/ 8 = 39

population sd = 12

Assuming that the data is normally distributed and also as the population sd is given, we will calcualate z stat

Step 4: Critical value

The z-critical values for a two-tailed test, for a significance level of α=0.05

zc = −1.96 and zc = 1.96

Step 5: Decision

As the z stat (-0.849) does not fall in the rejection area, we fail to reject the Null hypothesis.

.

Step 6: Conclusion

As we fail to reject the Null hypothesis, we do not have sufficient evidence to believe that that the average age of those receiving parking tickets is not same as the age of average age of licensed drivers in a county (i.e. population of drivers.)