Question 1068633: Passenger comfort is influenced by the amount of pressurization in an airline cabin. Higher pressurization allows a closer-to-normal environment and a more relaxed flight. A study by an airline user group recorded the corresponding air pressure on 30 randomly chosen flights. The study revealed a mean equivalent pressure of 8000 feet with a standard deviation of 300 feet.
Develop a 99% confidence interval for the population mean equivalent pressure.
How large a sample is needed to find the population mean within 25 feet at 95% confidence?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! CI is 8000+/-t df=29,0.995 *300/sqrt(30); t value is 2.756
interval width is 2.756*300/sqrt(30)=150.95
(7849,8151)
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interval is 25=z*300/sqrt(n)
I use z, because the sample size is large, and I can always then use t for that df and see if it changes the result.
25=1.96*300/sqrt(n)
25 sqrt(n)=1.96*300=588
sqrt(n)=588/25=23.52
square both sides
n=553.19 round to 554. With this size sample, t=z.
When I use this in the calculator for a t-test, I get an interval of +/-25.
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