SOLUTION: In a random sample of 24 ​people, the mean commute time to work was 30.8 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and
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Question 1129450: In a random sample of 24 people, the mean commute time to work was 30.8 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a t-distribution to construct a 95% confidence interval for the population mean mu. What is the margin of error of mu? Interpret the results.
The confidence interval for the population mean mu is left parenthesis comma right parenthesis .
(Round to one decimal place as needed.)
The margin of error of mean is:
(Round to one decimal place as needed.)
Interpret the results.
A.
It can be said that 95% of people have a commute time between the bounds of the confidence interval.
B.
With 95% confidence, it can be said that the commute time is between the bounds of the confidence interval.
C.
With 95% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.
D.
If a large sample of people are taken approximately 95% of them will have commute times between the bounds of the confidence interval.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
t df=23,0.975=2.069
s=7.1
ts/sqrt(n) is half interval or 2.069*7.1/sqrt(24)=3.0 ANSWER
(27.8, 33.8)units minutes
C
The purpose of a confidence interval is to define where the true mean lies, with a certain degree of confidence. The true mean is usually unknown and unknowable and either lies in or out of the interval. We don't know which, and it is a 100-0 type of issue, which is why we use confidence for where we think the true mean lies, not a probability.
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