4. Your boastful roommate claims that fans for the Chicago Bears (the city's football team) are simply more intelligent than the average person. With your newly-developed statistical tools, you decide to put this hypothesis to the test. You know that the standard intelligence quotient (IQ) score has a population mean of 100 with a standard deviation of 15. You find that a random sample of 121 Bears fans has an average IQ score of 103. Use this evidence to test your roommate's argument that Bears fans are more intelligent than the general population.

a) (0.125 points) What is the null hypothesis for this test?

b) (0.125 points) What is the alternative hypothesis for this test?

c) (0.125 points) Is this a one-sided or two-sided test? How do you know?

d) (0.125 points) What is the critical z-score of the test statistic given an level of 0.05?

e) (0.5 points) What is the value of the test statistic calculated from the sample results?

f) (0.25 points) What decision about the null hypothesis does your test lead to, and what does this indicate about the intelligence of Bears fans relative to the average person?

g) (0.5 points) Would your decision be different if you used an alpha level of .01? Explain.