2. The body mass index (BMI) of an individual is one measure that is used to judge whether an individual is overweight or not. A BMI between 20 and 25 indicates that one is at a normal weight. In a survey of 750 men and 750 women, the Gallup organization found that 203 men and 270 women were normal weight. Let population 1 be the men; population 2 be the women. (a) Construct a 90% confidence interval for the difference between the proportion of men proportion of women who are normal weight. (b) Interpret the interval in the form of a test of hypothesis with H0: p1 = p2.---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- (a) Compute p1^ and p2^. p1^ = = _____________; p2^ = = _____________ Conditions Required: The samples are obtained independently using simple random sampling. LET's ASSUME YES. n1p1^(1 - p1^) = _______________________. Is this 10? ___________. n2p2^(1 - p2^) = _______________________. Is this 10? ___________. Can you deduce that each sample size is less than 5% of its population size? Why? _____________________________________________________________________. USING TECHNOLOGY: The "TI83/84 CALCULATOR" PROCEDURE STAT > TESTS Choose (B): "2-PropZInt" Display: (___________, ___________) (b) Interpretation: Because this interval DOES / DOES NOT contain 0, we might conclude that there IS / IS NOT a difference in the proportion of men and women who are of normal weight. That is, we REJECT / DO NOT REJECT H0: p1 = p2.