3. The ABC Elementary School has 1,000 students. The principal of the school believes

that the average IQ of students at ABC is at least 110. To prove her point, she administers an IQ

test to 20 randomly selected students. Among the sampled students, the average IQ is 108 with

a standard deviation of 10. Based on these results, should the principal accept or reject her

original hypothesis? Assume a significance level of 0.01. (Assume that test scores in the

population are normally distributed)

a. Specify the null and the alternative hypotheses for the test

b. Given the significance level, find the critical value.

c. Calculate the value of the test statistic.

d. State the conclusion and interpret the results?

e. If, in fact the mean is 112 and standard deviation is 10.9, what will the probability of Type 2 error of our test be?