Twenty years ago 40 children were born in the same hospital in Denmark. Researchers classified the children by whether or not they were breast-fed for at least 3 months. They were interested in whether breast-feeding tends to increase IQ levels. Recently the 40 young adults were given IQ tests. The testers did not know which group a subject belonged to. The results are summarized below as part of the output for a two-sample t-test. Two-sample T for IQ Brstd N Mean StDev SE Mean Yes 18 113.4 14.6 3.4 No 22 103.5 15.2 3.2 T-Test of difference = 0 (vs >): T-Value = 2.09 P-Value = DF = 38.

(a) State the appropriate hypotheses in this case, defining any parameters you use.

(b) Somehow the p-value did not get printed. Use the Vassar applet to compute the p-value.

(c) Carefully state your conclusions based on these data. Use a level of significance of 5%.

(d) Would your conclusion change if we preferred to use a level of significance of 1% instead of 5%? Explain.

(e) What type of hypothesis testing error might you have made in reaching your conclusion in Part (c)?

(f) Given your conclusion in Part (c), can we reasonably conclude that it was the breast-feeding that was responsible for the difference in average IQ for the two groups? Explain.