SOLUTION: A beer producer wants to find out whether its existing bottling equipment is working to standards. 151 bottles were selected for testing: the average beer fill level is x̄ = 50.1m

Question 1202553: A beer producer wants to find out whether its existing bottling equipment is working to standards. 151 bottles were selected for testing: the average beer fill level is x̄ = 50.1mm and the sample variance s^2 = 4mm^2.
Determine the 99% confidence interval for the mean value.
Determine the 90% confidence interval for the variance.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
sample size is 151.
sample mean is 50.1 millimeters.
sample variance is 4 millimeters.
sample standard deviation is square root of 4 = 2 millimeters.
standard error is 2/sqrt(151) = 1.628 rounded to 4 decimal places.

critical t-score at 99% two-tailed confidence inteval with 150 degrees of freedom is plus or minus 2.609 rounded to 3 decimal places.

critical t-score at 90% two-tailed confidence interval with 150 degrees of freedom is plus or minus 1.656 rounded to 3 decimal places.

mean of the sample is assumed to be 50.1.
mean of the variance is assumed to be 4.

use the t-score formula to find the raw score of the confidence interval.
formula is t = (x-m)/s
t is the t-score.
x is the critical raw score.
m is the mean of the sample.
s is the standard error.

for the mean, the formula becomes:
2.609 = (x - 50.1) / 1.628 on the high side.
solve for x to get x = 2.609 * 1.628 + 50.1 = 54.35 rounded to 2 decimal places.
-2.609 = (x - 50.1) / 1.628 on the low side.
solve for x to get x = -2.609 * 1.628 + 50.1 = 45.85 rounded to 2 decimal places.

for the variance, the formula becomes:
1.656 = (x - 4) / 1.628 on the high side.
solve for x to get x = 1.656 * 1.628 + 4 = 6.7 rounded to 2 decimal places.
-1.656 = (x - 4) / 1.628 on the low side.
solve for x to get x = -1.656 * 1.628 + 4 = 1.30 rounded to 2 decimal places.

your 99% confidence interval for the mean is 45.85 to 54.35.
your 99% confidence interval for the variance is 1.30 to 6.70.

i'm pretty sure about the mean of the sample.
i think that's the way to analyze the variance of the sample, but i'm not surre.

RELATED QUESTIONS
(a) The quality control department of Red Stripe Jamaica Ltd is interested in estimating... (answered by stanbon)

3. You are visiting Dad�s Root Beer Plant in Oakland. You are asked by the plant... (answered by richwmiller)

The Hudson Valley Bottling Company distributes root beer in bottles labeled 32 ounces.... (answered by stanbon)

A beer-bottling company ordered 2100 more 12-ounce bottles than 1-quart bottles. The cost (answered by mananth)

At the pure water bottling company one machine can produce 180 bottles in 5 hours and a... (answered by stanbon)

) A brewery has a beer dispensing machine that dispenses beer into the company's 12... (answered by CPhill)

what is the anser for the following, 60% of the students in the computer course passed... (answered by stanbon)

good morning. my brain is going blank on my problems, can you help me on this one... (answered by stanbon)

Please help with this calculation, please show full workings. Many thanks. The... (answered by lynnlo)