SOLUTION: (Give your answers correct to TWO (2) decimal places) In a time and motion study, the amount of time required to paint a 10-foot by 10-foot room is measured for 25 painters. The

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Question 1175516: (Give your answers correct to TWO (2) decimal places)
In a time and motion study, the amount of time required to paint a 10-foot by 10-foot room is measured for 25 painters. The sample mean is calculated and found to be 72 minutes. If we assume that the population standard deviation is 5 minutes,
(a) find the 95% confidence interval estimate of the mean time for all painters to paint a 10-foot by 10-foot room.
Answer:the 95% confidence interval estimate of the mean time for all painters to paint a 10-foot by 10-foot room is from ____ minutes to ____minutes.

(b) find the 97% confidence interval estimate of the mean time for all painters to paint a 10-foot by 10-foot room.
Answer: the 97% confidence interval estimate of the mean time for all painters to paint a 10-foot by 10-foot room is from____ minutes to____minutes.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
sample size is 25
sample mean is 72 minutes
population standard deviation is 5 minutes.

standard error = standard deviation / square root of sample size = 5 / sqrt(25) = 5/5 = 1.

z-score = (x - m) / s

x is the raw score
m is the raw mean
s is the standard error.

at two tailed confidence level, the tails on each end of the confidence interval are 2.5%.

the critical z-score is therefore equal to plus or minus 1.96.

solve for the high raw score as follows:

start with 1.96 = (x - 72) / 1

solve for x to get x = 1.96 * 1 + 72 = 73.96.

solve for the low raw score as follows:

start with -1.96 = (x - 72) / 1

solve for x to get x = -1.96 * 1 + 72 = 70.04

your answer for question (a) is 70.04 to 73.96 minutes.

with a two tailed 97% confidence level, the tails on each end of the confidence interval are 1.5%.

the critical z-score becomes plus or minus 2.17.

solve for the low and high raw score in the same manner as you did the the 95% confidence interval.

you will get the low score equal to 69.83 and the high score equal to 74.17.

visually, this looks like this.

first 95% confidence interval, then 97% confidence interval.

when dealing with the mean of a sample, you do not use the standard deviation.

you use the standard error.

the standard error is defined as the standard deviation of the distribution of sample means.

here's a reference.

https://www.investopedia.com/terms/s/standard-error.asp