A Smallville police officer was interested in whether the average age of those receiving parking tickets in Smallville differed from that of the average age of the population of licensed drivers in Smallville. The average age for licensed drivers in Smallville is µ= 42.6, σ= 12 and the distribution is approximately normal. The police officer obtained a random sample of N = 25 drivers in Smallville, who received parking tickets. The average age for those drivers was M= 40.5. Test using a 5% (α=.05) significance level.

Using this information, please answer all of the following questions:

1. What is the appropriate hypothesis test for analyzing this data? Why is it appropriate?

2. Complete the hypothesis test and answer all of the following questions to answer whether the average age of drivers receiving parking tickets differs from the population of drivers in Smallville:

a. What are the null and alternative hypotheses (H_o and H_a)? 

b. What are the assumptions that need to be met for the hypothesis test?

c. What is the  test statistic and the p-value of the test? Note: You may use the normal calculator to calculate the p-value: z-Table - Normal Distribution Calculator.

d. What is your decision regarding whether or not to reject the null hypothesis? What does that mean in terms of the ages of the drivers? Note: To do this, please compare the stated α with the p-value.

3. Given the conclusion found in #2d, which type of error (Type I or Type II) is a possibility? Why? 

4. Given the possible type of error (Type I or Type II) made in this situation, what could researchers do to reduce the risk of this error?