A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet.Subjects were randomly assigned to a treatment group and a control group.The mean blood pressure was determined for each group,and a 90% confidence interval for the difference in the mean between the treatment group and the control group, $\mu _ { \mathrm { t } } - \mu _ { \mathrm { C } }$ was found to be (-26,-6).
A)We are 90% confident that a randomly selected subject in the treatment group had a blood pressure between 6 and 26 points lower than a randomly selected subject in the control group.
B)We are confident that 90% of all people who follow the particular diet will have a blood pressure between 6 and 26 points lower than people who do not follow the diet.
C)We know with 90% confidence that people who follow the diet have an average blood pressure between 6 and 26 points lower than people who do not follow the diet.
D)We know with 90% confidence that people who follow the diet have an average blood pressure between 6 and 26 points higher than people who do not follow the diet.
E)We know that 90% of all experiments done on the population will show that the average blood pressure for people who follow the diet is between 6 and 26 points lower than the average blood pressure for people who do not follow the diet.

Question

Quizplus · Accepted Answer

The confidence interval tells us that we are 90% confident that the true difference in mean blood pressure between the treatment and control groups is between -26 and -6. Since the lower bound of the confidence interval is negative, we are confident that the treatment group has a lower mean blood pressure than the control group. Therefore, we can say that we know with 90% confidence that people who follow the diet have an average blood pressure between 6 and 26 points lower than people who do not follow the diet. Option A is incorrect because we cannot make conclusions about individual subjects based on a confidence interval. Option B is incorrect because we cannot make a statement about individuals who follow the diet, only about the average blood pressure of the treatment group compared to the control group. Option D is incorrect because the confidence interval tells us that the treatment group has a lower mean blood pressure than the control group, not a higher one. Option E is incorrect because a confidence interval applies to the specific sample and cannot be extended to generalize to all experiments done on the population.

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A Researcher Wishes to Determine Whether People with High Blood $\mu _ { \mathrm { t } } - \mu _ { \mathrm { C } }$