In estimating a population mean with a confidence interval based on a random sample X1....,Xn from a Normal distribution with an unknown mean and a known variance, Compare the length of the 95% and 90% confidence intervals for the unknown mean based on X1,.,Xn. The 95% confidence interval is wider than the 90% confidence interval O Both 95% and 90% confidence intervals have the same length O The 90% confidence interval is wider than the 95% confidence interval D 10 2 7 In a recent study, a random sample of 1200 Americans were tested for magnesium level. In total, 540 were found to have deficient magnesium levels. American Medical Association claims that 50% of Americans are magnesium deficient. Find a 95% confidence interval for the true proportion of Americans who have deficient magnesium levels and determine if there is any evidence to suggest that the percentage of Americans who have deficient magnesium levels is different from this value? Let p be "true proportion of Americans who have deficient magnesium levels". 95% C.I. is (.4219, .4781). Since 0.5 does not lie in this C.I., there is evidence to suggest that p is not different from 0.5. 95% C.I. is (.4129. .5351). Since 0.5 lies in this C.I., there is evidence to suggest that p is not different from 0.5. 95% C.I. is (.4129. .5351). Since 0.5 lies in this C.I., there is evidence to suggest that p is different from 0.5. 95% C.I. is (.4219. .4781). Since 0.5 does not lie in this C.I., there is evidence to suggest that p is different from 0.5. D 19 A University of Florida economist conducted a study of Virginia elementary school lunch menus. During the state-mandated testing period, school lunches average 863 calories. The economist claimed that after the testing period end, the average calories content of Virginia school lunches dropped significantly. Set up the null and alternative hypothesis to test the economist's claim. Let m be the average calories content of Virginia school lunches. O HO: m = 863, Ha: m is not equal to 863 O HO: m = 863, Ha: m > 863 O HO: m - 863, Ha: m