1. A psychologist would like to estimate the average IQ ofCanadians. (IQ scores are known to follow a normal distributionwith standard deviation 15.) She takes a sample of 49 Canadians andmeasures a sample mean IQ of 107.34 and a sample standard deviationof 17.36.
(a) Use the information above to calculate a 92% confidenceinterval to estimate the average IQ of Canadians.
(b) Interpret the confidence interval obtained in part (a).
(c) Suppose the researcher also wishes to test thehypotheses
H0 :?=103 vs. ??=103
at the 0.08 significance level. Is this possible to do with theconfidence interval calculated in part (a)? If so, what is thecorrect conclusion? If not, why not?
(d) Suppose the researcher also wishes to test thehypotheses
H0 :?=105 vs. ?>105
at the 0.08 significance level. Is this possible to do with theconfidence interval calculated in part (a)? If so, what is thecorrect conclusion? If not, why not?
