Question

A random sample of 14 ​men's resting pulse rates showed a mean of 71.5 beats per minute and standard deviation of 19.9. Assume that pulse rates are Normally distributed. Use the table to complete parts​ (a) through​ (c) below. LOADING... Click the icon to view the​ t-table. a. Find a​ 95% confidence interval for the population mean pulse rate of​ men, and report it in a sentence. Choose the correct answer below​ and, if​ necessary, fill in the answer boxes to complete your choice. ​(Type integers or decimals rounded to the nearest tenth as needed. Use ascending​ order.)

A. There is a​ 95% chance that all resting pulse rates will be between nothing and nothing.

B. We are​ 95% confident that the population mean resting pulse rate is between nothing and nothing.

C. We are​ 95% confident that the sample mean resting pulse rate is between nothing and nothing.

D. The requirements for constructing a confidence interval are not satisfied.

Answer 1

sample mean, xbar = 71.5
sample standard deviation, s = 19.9
sample size, n = 14
degrees of freedom, df = n - 1 = 13

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.16

ME = tc * s/sqrt(n)
ME = 2.16 * 19.9/sqrt(14)
ME = 11.488

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (71.5 - 2.16 * 19.9/sqrt(14) , 71.5 + 2.16 * 19.9/sqrt(14))
CI = (60.0 , 83.0)

B. We are​ 95% confident that the population mean resting pulse rate is between 60.0 and 83.0