4. For the following problem, test the difference between two means by doing the following: a) Identify the claim and state the null and alternative hypotheses. b) Determine the degrees of freedom. c) Calculate the standardized test statistic. d) Determine the p-value. e) Decide to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. f) Was this an experimental or an observational study? Can you think of a potential lurking variable?

Problem: Breast- feeding helps IQ?: A Danish study of individuals born at a Copenhagen hospital between 1959 and 1961 reported higher mean IQ scores for adults who were breast-fed for longer lengths of time as babies ( E. Mortensen et al., JAMA, vol. 287, pp. 2365- 2371, 2002). The mean IQ score was 98.1(s=15.9) for the 272 subjects who had been breast- fed for no longer than a month and 108.2 (s=13.1) for the 104 subjects who had been breast-fed for 7- 9 months.

Use an inferential method (significance test) to analyze whether the corresponding population means differ, assuming the population standard deviations are equal. (12 marks)