Question

A soft drink machine is regulated so that the amount of drink it dispenses follows a normal distribution with a known standard deviation of the drinks dispensed of 20 milliliters.
A random sample of 30 drinks from the machine had an average volume of 373 milliliters. Determine a 95% confidence interval for the average amount of all drinks dispensed by this machine.

Here I know the formula for confidence intervals but not sure of how to proceed with the question. Can any 1 help me out?

Answer 1

lets list out whats given :

\(\sigma = 20\)
\(n = 30\)
\(\overline{x} = 373\)

Answer 2

Confidence interval = \(\large \overline{x} \pm Z^* \frac{\sigma}{\sqrt{n}}\)

Answer 3

simply plugin the values

Answer 4

oh....simple calculation. But is there any specific table for calculating confidence interval....I have no idea.

Answer 5

yes :)

http://www.math.upenn.edu/~chhays/zscoretable.pdf

Answer 6

look at the zscore value when the area is approximately \(0.95\)

Answer 7

thanks a lot. I have to solve many problems based on confidence intervals...it will be useful for me!!!

Answer 8

ack.. I was wrong earlier,
for 95% CI, the zscore is \(1.64\)

Answer 9

so, \(\large Z^* = 1.64\)

Answer 10

np :)

Answer 11

ok....ty!!!!

Answer 12

I have one more concern....what happens if the 30 samples alone has different standard deviation. Should we calculate the confidence interval for both and subtract it?

Answer 13

good question :)

Answer 14

let me rephrase ur question a bit

Answer 15

you're asking :-

"If we know both population standard deviation and the sample standard deviation, which one we need to use for computing Confidence Intervals ?"

Answer 16

thats the question, right ?

Answer 17

spot on!!!!!!

Answer 18

If the population is not too much skewed, then the sample standard deviation should MATCH almost perfectly with population standard deviaiton

Answer 19

here is the rule of thumb :-
if you knw populaiton standard deviation, USE it !!

if you dont knw population standard deviaition, compute standard deviation from sample

Answer 20

In general, you will not have access to populaiton parameters... cuz when u do surveys u wont knw upfront what their mean/standard deviation will be

Answer 21

so we will be computing sample standard deviation almost all the time

Answer 22

say, if both population S.D and sample S.D are given in a problem....what should we do??

Answer 23

say, sample SD is 20 and population SD is 23. should we solve the problem with sample SD?