2. Suppose that a particular SAT coaching company advertises
that their $1500 SAT Review course will
improve scores by 50 points on average.
a. Write the null and alternative hypotheses using both words and
symbols.
b. Suppose that the FTC gathers information from a very large random sample
of patrons and finds that the average improvement in SAT scores
is x = 48 points, with a p-
value for this result of 0.002. The Federal Trade Commission is
gathering evidence to see if this
advertising claim is accurate. If the FTC finds evidence that
the average score improvement is
less than 50 points, the agency will file a lawsuit against the
company for false advertising.
Are the results statistically significant at the level?
c. If any error were to occur in the decision to reject or fail
to reject,
would it be a Type I error or a Type II error?