Question: A researcher wishes to test the hypothesis that the mean IQ at a particular university is different from the average of 100. The researcher obtains a sample of 100 students. The mean of this sample, is 103.6. The population standard deviation of IQ scores is 15.0.

(a) State the null hypothesis and alternative hypothesis in mathematical notations,

(b) Find the test statistic,

(c) Find the p value for a two-tailed test.

(d) For a two-tailed test with a = 5%, what arc the critical values?

(c) What should the researcher decide given the above results?

(f) If the researcher's conclusion above is an error, what type of error would that be'?

(g) Repeat the hypothesis test above with a 1%: find the test statistic, p value, critical values, and state the conclusion.

(h) If the researcher's conclusion above is an error, what type of error would that be?