Question

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 either a treatment group (the diet) or a control group (no diet).The mean blood pressure was determined for each group, and a 95% confidence interval for the difference in the means for the treatment group versus the control group, ?t - ?c, was found to be (-21, -6).
The probability that the mean blood pressure for those on the diet is lower than for those not on the diet is0.95

Answer 1

Answer:

We are 95% confident that the average blood pressure of those who follow the diet is between 6 and 21points lower than the average for those who do not follow the diet.

 TRUE, the confidence interval founded was $-21 \leq \mu_t -\mu_c \leq -6$, on this case makes sense say that the blood pressure for the people with the diet is lower than the control group between 6 and 27 points.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

2) Select the correct option

The probability that the mean blood pressure for those on the diet is lower than for those not on the diet is 0.95.

FALSE, that's not the correct interpretation for the results obtained on the confidence interval for the difference of means.

We are 95% confident that the average blood pressure of those who follow the diet is between 6 and 21 points higher than the average for those who do not follow the diet.

FALSE, the confidence interval was for $\mu_t -\mu_c$ and we know that $-21 \leq \mu_t -\mu_c \leq -6$, so no makes sense say that the blood pressure for the people with the diet is higher than the control group.

We are 95% confident that the average blood pressure of those who follow the diet is between 6 and 21 points lower than the average for those who do not follow the diet.

 TRUE, the confidence interval founded was $-21 \leq \mu_t -\mu_c \leq -6$, on this case makes sense say that the blood pressure for the people with the diet is lower than the control group between 6 and 27 points.

Since all of the values in the confidence interval are less than 0, we are unable to conclude that there is a difference in blood pressure for those who follow the diet and those who do not.

FALSE, we are able to conclude about the experiment between the diet and the control group