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2. The weight gain of women during pregnancy has an important effect on the birth weight of their children. If the weight gain is not adequate, the infant is more likely to be small and will tend to be less healthy. In a study conducted in two countries, weight gains (in kilogram) of women during the third trimester of pregnancy were measured. The results are summarized in the following table. Country 71 g 32 Egypt 6 3.8 5.76 Kenya 10 3.3 3.61 (a) Test for any dierence on the average weight gains between two countries using a: = .01. State the null and alternate hypotheses, and report the value of the test statistic, and the critical value used to conduct the test. Report your decision regarding the null hypothesis and your conclusion in the context of the problem. Consider two cases, equal and unequal variances. (b) Find a 95% confidence interval for /1 - /2 and interpret this interval. Assume population variances are equal