Question

A statistics instructor randomly selected four bags of​ oranges, each bag labeled 10​ pounds, and weighed the bags. They weighed 10.3, 10.2, 10.3, and 10.4 pounds.   

Assume that the distribution of weights is Normal. Find a​ 95% confidence interval for the mean weight of all bags of oranges. Use technology for your calculations.

a. Choose the correct interpretation of the confidence interval. Is the answer A,B,C or D and the 2 numbers.

A.We are​ 95% confident that the sample mean is between Answer ____ and ____.

B.We are​ 95% confident the population mean is between Answer ____ and ____.

C.There is a​ 95% chance that all intervals will be between Answer ___ and ___

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

(Type integers or decimals rounded to the nearest thousandth as needed. Use ascending​ order.)

Answer 1

sample mean, xbar = 10.3
sample standard deviation, s = 0.0817
sample size, n = 4
degrees of freedom, df = n - 1 = 3

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 3.182

ME = tc * s/sqrt(n)
ME = 3.182 * 0.0817/sqrt(4)
ME = 0.13

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (10.3 - 3.182 * 0.0817/sqrt(4) , 10.3 + 3.182 * 0.0817/sqrt(4))
CI = (10.17 , 10.43)

A.We are​ 95% confident that the popultion mean is between Answer 10.170 and 10.430