Question

This Quiz: 22 pts possit Use the standard normal distribution or the t-distribution to construct a 99% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 40 people, the mean body mass index (BMI) was 26.9 and the standard deviation was 6.03. O A. Use a normal distribution because the sample is random, the population is normal, and is known O B. Use a t-distribution because the sample is random, the population is normal, and is unknown. O c. Use a normal distribution because the sample is random, n 230, and is known D. Use a t-distribution because the sample is random, n 30, and a is unknown O O E. Neither a normal distribution nor a t-distribution can be used because either the sample is not random, or n < 30, and the population is not known to be normal. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice cc A. The 99% confidence interval is ) (Round to two decimal places as needed.) B. Neither distribution can be used to construct the confidence interval. LIO Opt Interpret the results. Choose the correct answer below. atoi O A. It can be said that 99% of people have a BMI between the bounds of the confidence interval. O B. With 99% confidence, it can be said that the population mean BMI is between the bounds of the confidence interval. O c. If a large sample of people are taken approximately 99% of them will have a BMI between the bounds of the confidence interval. ols Click to select your answer. Save for Later

Answer 1

solution:

sample size =n= 40

sample mean = $\bar X$ = 26.9

sample standard deviation = S = 6.03

As the sample is randomly selected and standard deviation of the population is unknown so we use the t-distribution.

correct answer

B ) using a t distribution because the sample is random , the population is normal and the $\sigma$ is unknown

step 2

significance level =$\alpha$= 1 - 0.99 = 0.01

degree of freedom = df = n - 1 = 40-1 = 39

critical value of t by using the t table =
ta/2,df = 0.01/2,39 = 2.708

margin of error(E) =
tal2 ur v = 2.708 • bot – 2.58

confidance interval = $\bar X \pm E$

lower bound of interval = 26.9 - 2.58 = 24.32

upper bound of interval = 26.9 + 2.58 = 29.48

correct choice is A) The 99% confidence interval is (24.32, 29.48)

part c)

interpretation of confidance interval

B) with 99% confidance , it can be said that the population mean BMI is between the bounds of confidence interval.