1.
(a) The DASH study is generally considered the best of these randomized controlled experiments. The DASH study found a correlation of 0.3 between salt consumption and (systolic) blood pressure. The standard deviation of salt consumption is 2.5 g/day and the standard deviation of systolic blood pressure is 10 mm Hg. Suppose a person cuts the amount of salt in his/her diet by 3 g/day. How much will his/her systolic blood pressure go down?
(b) What is the slope of the regression line for predicting systolic blood pressure based on salt consumption?
2. A 1986 study found the average sensitivity of a home pregnancy test to be 80%, and the average specificity to be 68%.
(a). If a pregnant woman takes the test, what is the probability that she will get a negative reading?
(b). Suppose that the prior probability of a woman being pregnant is 30%. If she takes a hojme pregnancy test and the result is positive, what is the posterior probability that shw is pregnant, given the positive result?
(c). In one month, 50 babies are delivered in Hospital A, while 30% babies are delivered in hospital B. For which hospital is it more likely that over 55% of the babies were boys? Or is the probability the same for each hospital?
3. According to the Natioanl Health and Nutrition Examination Survey, the average systolic blood pressure amoung adult males in the united states is 129 mm Hg and the standard deviation is 19.8 mm Hg. The distribution of systolic blood pressure is not perfectly normal, but it's reasonably close.
(a). An individual may be classified as hypertensive (having high blood pressure) if his systolic blood pressure is above 140 mm Hg. Based on the information above, what percent of adult males in the United States are hypertensive?
(b). If I collect a random sample of five men, what is the probability that exactly 2 of them will be hypertensive?
(c). If I collect a random sample of 50 men, about __________ of them will be hypertensive, give or take _________.
(d). If I collect a random sample of ten men, what is the probability that their average systolic blood pressure will be above 140 mm Hg?
(e). A researcher proposes that instead of 140 mm Hg, a man should be classified as hypertensive if his systolic blood pressure is above the 90th percentile. What blood pressure cutoff is the researcher proposing?
(a) The DASH study is generally considered the best of these randomized controlled experiments. The DASH study found a correlation of 0.3 between salt consumption and (systolic) blood pressure. The standard deviation of salt consumption is 2.5 g/day and the standard deviation of systolic blood pressure is 10 mm Hg. Suppose a person cuts the amount of salt in his/her diet by 3 g/day. How much will his/her systolic blood pressure go down?
(b) What is the slope of the regression line for predicting systolic blood pressure based on salt consumption?
2. A 1986 study found the average sensitivity of a home pregnancy test to be 80%, and the average specificity to be 68%.
(a). If a pregnant woman takes the test, what is the probability that she will get a negative reading?
(b). Suppose that the prior probability of a woman being pregnant is 30%. If she takes a hojme pregnancy test and the result is positive, what is the posterior probability that shw is pregnant, given the positive result?
(c). In one month, 50 babies are delivered in Hospital A, while 30% babies are delivered in hospital B. For which hospital is it more likely that over 55% of the babies were boys? Or is the probability the same for each hospital?
3. According to the Natioanl Health and Nutrition Examination Survey, the average systolic blood pressure amoung adult males in the united states is 129 mm Hg and the standard deviation is 19.8 mm Hg. The distribution of systolic blood pressure is not perfectly normal, but it's reasonably close.
(a). An individual may be classified as hypertensive (having high blood pressure) if his systolic blood pressure is above 140 mm Hg. Based on the information above, what percent of adult males in the United States are hypertensive?
(b). If I collect a random sample of five men, what is the probability that exactly 2 of them will be hypertensive?
(c). If I collect a random sample of 50 men, about __________ of them will be hypertensive, give or take _________.
(d). If I collect a random sample of ten men, what is the probability that their average systolic blood pressure will be above 140 mm Hg?
(e). A researcher proposes that instead of 140 mm Hg, a man should be classified as hypertensive if his systolic blood pressure is above the 90th percentile. What blood pressure cutoff is the researcher proposing?