Question

A certain brand of apple juice is supposed to have 64 ounces of juice. The filling machine is not precise, and the exact amount of juice varies from bottle to bottle. Because the penalty for under filling is severe, the quality control manager wishes to verify the mean amount of juice in each bottle. She takes a random sample of 25 bottles, finding a mean of 63.6 ounces and a standard deviation of 0.8 ounces. The data from the 25 bottles appears unimodal and symmetric.

Find a 90% confidence interval for the true mean number of ounces of apple juice that is filled.

Due to the different methods, select the best possible answer.

Group of answer choices

A (54.8, 65.7)

B (58.1, 65.1)

C (63.3, 63.9)

D (61.2, 66.8)

Answer 1

Given n = 25

sample mean Xbar = 63.6

Sample standard deviation s = 0.8

  

  90% confidence interval for the true mean number of ounces of apple juice that is filled is

Xbar - E < < xbar + E

Where E = t​​​​​​a/2*( s/√n)

For a = 0.10 , d.f = n -1 = 24

t​​​​​​a/2,n-1 = t​​​​​​0.05,24 = 1.71

E = 1.71*(0.8/√25) = 0.27

63.6 - 0.27 < < 63.6 + 0.27

63.3 < < 63.9

Option C is correct