In a random sample of 27 people, the mean commute time to work was 31.2 minutes

Question

In a random sample of 27 people, the mean commute time to work was 31.2 minutes and the standar deviation was 7.3 minutes. Assume the population is normally distributed and use a t-distribution to construct a 95% confidence interval for the population mean What is the margin of error of ? Inter the results The confidence interval for the population mean is Round to one decimal place as needed.) The margin of error of is Round to one decimal place as needed.) Interpret the results. A, with 95% confidence, it can be said that the commute time is between the bounds of the O B. If a large sample of people are taken approximately 95% of them will have commute times ° C. It can be said that 95% of people have a commute time between the bounds of the confidence ( D. With 95% confidence it can be said that the population mean commute time is between the confidence interval between the bounds of the confidence interval. interval. bounds of the confidence interval.

Explanation / Answer

Sol:

sample mean=31.2

sample sd=7.3

sample size=n=27

alpha=95%=0.95

n-1=27-1=26

alpha=1-0.95=0.05

alpha/2=0.05/2=0.025

t crit=2.056

95% Confidence interval for population mean is

samplemean-tcri(samplesd)/sqrt(n),samplemean+tcri(samplesd)/sqrt(n)

31.2-2.056(7.3/sqrt(27),31.2+2.056(7.3/sqrt(27)

28.3,34.1

lower limit=28.3

upper limit=34.1

confidence interval of the population mean is 28.3,34.1

Margin of error=tcri(samplesd)/sqrt(n)

=2.056(7.3/sqrt(27)

=2.9

With 95% confidence,it can be said that the population mean commute time is between the bounds of the confidence interval

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