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.

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

Answer 1

The correct answer is b.

Explanation:

Hello!

The objective is to determine if following a certain diet reduces high blood pressure. The treatment and control were randomly assigned establishing two independent samples and two study variables.

X₁: Blood pressure of a person from the treatment group.

X₂: Blood pressure of a person from the control group.

With the blood pressure data of both groups, the difference of the population means "μ₁ - μ₂" was estimated by a 95% confidence interval.

Obtaining [-21;-6]

A little reminder: In general, the 95% level of confidence means that if you were to make 100 confidence intervals you'd expect that 95 will contain the true value of the parameter you intended to estimate, in this case, the parameter is "μ₁ - μ₂".

So, with a confidence level of 95%, you'd expect that the interval [-21;-6] contains the value of the difference between the average blood pressure of people that followed the diet and the average blood pressure of people that didn't follow the diet.

Since the two limits of the interval are negative, it seems to suggest that the blood pressure of the treatment group is lower than that of the control group. This, however, cannot be assured just by observing the interval. The most appropriate procedure, when viewing this interval, is to carry out a statistical test to confirm the suspicion, with statistical hypothesis H₀: μ₁ ≥ μ₂ vs. H₁: μ₁ < μ₂.

The correct answer is b.

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