The mean IQ for the entire population in any age group is supposed to be 100. Suppose the IQ scores of 72 12 ^th graders in Columbus are measured and the sample mean is found to be 103.4 and the sample standard deviation is 20.2. Do the scores provide good evidence that the mean IQ of this population is not 100?

A) State the null (H ₀ ) and alternative (H ₁ ) hypotheses.

B) If the null hypothesis is true, the sample mean has approximately a Normal distribution with mean ________ and standard deviation _________.

C) Give the test statistic for the data.

D) Find the P-value for this significance test.

E) Summarize the conclusion in the context of this problem.

F) Describe a Type I and Type II error in the context of this problem.