Question

Use the standard nomal distribution or the distribution to construct a 95% confidence interval for the population mean. Justily your decisioni neither distribution can be used, explain why. Interpret the results In a random sample of 41 people, the mean body mass index (BMI) was 27.8 and the standard deviation was 6.11 Which distribution should be used to construct the confidence interval? Choose the correct answer below. O A Use a distribution because the sample is random, na 30, and is unknown OB. Use a t-distribution because the sample is random, the population is normal, and is unknown OC. Use a normal distribution because the sample is random, the population is normal, and an is known. OD. Use a normal distribution because the sample is random, 230, and is known. OE. Nolther a normal distribution nora -distribution can be used because either the sample is not random, or < 30, and the population is not known to be normal Select the correct choice below and necessary, fi in any answer boxes to complete your choice. OA. The 95% confidence interval is (Round to two decimal places as needed.) OB. Neither distribution can be used to construct the confidence interval Interpret the results. Choose the correct answer below. O A. If a large sample of people are taken approximately 5% of them will have a BMI between the bounds of the confidence interval OB. With 95% confidence, it can be said that the population mean BMI is between the bounds of the confidence interval Click to select your answer

Answer 1

a) option A is correct:

O A Use a distribution because the sample is random, n 230, and is unknown

b)

sample mean 'x̄=		27.6000
sample size    n=		41
std deviation s=		6.1100
std error ='sx=s/√n=6.11/√41=		0.9542

for 95% CI; and 40 df, value of t=		2.021
margin of error E=t*std error    =		1.93
lower bound=sample mean-E =		25.6714
Upper bound=sample mean+E =		29.5286
from above 95% confidence interval for population mean =(25.67<μ<29.53)

option A is correct :blanks are 25.67 and 29.53

c)

option B is correct: with 95% confidence , it can be said that the population mean BMI is between the bounds of the confidence interval.