Students participating in a drug education program are given a drug awareness test at the beginning of the program. The mean score (µ) for the population of 526 students is 61, with a standard deviation (σ) of 12. As program director, you're curious as to how parents of the students perform on the drug awareness test and whether or not they are significantly different from the students. Selecting a random sample of 50 parents, you administer the test and discover a mean drug awareness score (X) of 56. Assume that you're working at the .05 level of significance.
a. State an appropriate null hypothesis.
b. What is the value of the calculated test statistic (Z)?
c. State your conclusion.