Question

The daily caloric intake for samples of adult males and females have these statistics:

Sample Size Mean Standard Deviation
Males 15 2700 500
Females 10 2200 300

A 99% confidence interval for the difference in the true mean daily caloric intake of adult males and females is calculated. Which is a correct interpretation of this interval?

A) In repeated samples of 15 adult males and 10 adult females, 99% of similarly constructed intervals will contain the difference in true mean daily caloric intake between adult males and females.
B) In repeated samples of 15 adult males and 10 adult females, 99% of similarly constructed intervals will contain the difference in sample mean daily caloric intake between adult males and females.
C) The probability that μ1 - μ2 lies in the calculated interval is 0.99.
D) Approximately 99% of samples of 15 adult males and 10 adult females will have a difference in daily caloric intake between the lower and upper endpoints of the calculated confidence interval.

Answer 1

Answer on Question #84953 – Math – Statistics and Probability

Question

The daily caloric intake for samples of adult males and females have these statistics:

Sample Size Mean Standard Deviation

Males 15 2700 500

Females 10 2200 300

A 99% confidence interval for the difference in the true mean daily caloric intake of adult males and females is calculated. Which is a correct interpretation of this interval?

A) In repeated samples of 15 adult males and 10 adult females, 99% of similarly constructed intervals will contain the difference in true mean daily caloric intake between adult males and females.

B) In repeated samples of 15 adult males and 10 adult females, 99% of similarly constructed intervals will contain the difference in sample mean daily caloric intake between adult males and females.

C) The probability that $\mu_1 - \mu_2$ lies in the calculated interval is 0.99.

D) Approximately 99% of samples of 15 adult males and 10 adult females will have a difference in daily caloric intake between the lower and upper endpoints of the calculated confidence interval.

Solution

The confidence interval $\Delta$ is defined as such an interval that

$$P(\mu_1 - \mu_2 \in \Delta) = 0.99$$

Hence the answer is C).

Answer: C) The probability that $\mu_1 - \mu_2$ lies in the calculated interval is 0.99.

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