1. Observational studies suggest that moderate use of alcohol reduces heart attacks, and that red wine may have special benefits. One reason may be that red wine contains polyphenols, substances that do good things to cholesterol in the blood and so may reduce the risk of heart attacks. In an experiment, healthy men were assigned at random to drink half a bottle of either red or white wine each day for two weeks. The level of polyphenols in their blood was measured before and after the two week period. Here are the percent changes in level for the subjects in both groups. Red 3.5 8.1 7.4 4.0 0.7 4.9 8.4 7.0 5.5 White 3.1 0.5 -3.8 4.1 -0.6 2.7 1.9 -5.9 0.1 a. Is there good evidence that red wine drinkers gain more polyphenols on average than white wine drinkers? b. Does this study give reason to think that it is drinking red wine, rather than some lurking variable, that causes the increase in blood polyphenols? Justify your answer. c. Calculate and interpret a 95% confidence interval for the difference in mean polyphenols levels.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
1. Observational studies suggest that moderate use of alcohol reduces heart attacks, and that red wine may have special benefits. One reason may be that red wine contains polyphenols, substances that do good things to cholesterol in the blood and so may reduce the risk of heart attacks. In an experiment, healthy men were assigned at random to drink half a bottle of either red or white wine each day for two weeks. The level of polyphenols in their blood was measured before and after the two week period. Here are the percent changes in level for the subjects in both groups.
Red 3.5 8.1 7.4 4.0 0.7 4.9 8.4 7.0 5.5
White 3.1 0.5 -3.8 4.1 -0.6 2.7 1.9 -5.9 0.1
a. Is there good evidence that red wine drinkers gain more polyphenols on average than white wine drinkers?
b. Does this study give reason to think that it is drinking red wine, rather than some lurking variable, that causes the increase in blood polyphenols? Justify your answer.
c. Calculate and interpret a 95% confidence interval for the difference in
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