Hypothesis Test Problem
A school had decided to hire a new vice principal. A recent issue of the NEA magazine stated that the average vice principal salary for a school of similar size is $60,000. At the request of the Board of Education, the principal conducts his own survey of vice principal's salaries. His survey of 25 schools revealed an average salary or $72,000 and a standard deviation of $9,000. Perform a hypothesis test at a 5% significance level to test the magazine's claim.
a. What is the appropriate sampling distribution to use?
b. State the null and alternative hypotheses.
c. State the decision rule at a significance level of 5% show all calculations
d. Illustrate all key numbers and areas on a graph.
e. What decision should the school principal make?
f. What type of error can possibly be made with the decision in part (e)?
g. What is the value of the Maximum Tolerable Error for this problem?