In a random sample of 20 people, the mean commute time to work was 31.7 minutes and the standard 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 mu. what is the margin of error of mu? interpret the results.

Solution: We are given:

x bar=31.7

s = 7.3

n=20

The 95% confidence interval for the population mean is given below:

xbar +-

31.7 +- (2.093 x )

31.7 +- 3.42

[31.7-3.42,31.7+3.42]

[28.28 ,35.12 ]

Therefore the 95% confidence interval for the population mean is:

28.28≤μ≤35.12

The margin of error is 3.42

There is 95% chance that the confidence interval 28.28≤μ≤35.12 contains the true population mean.

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step-by-step explanation: