In a random sample of 18 people, the mean commute time to work was 33.1 minutes and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a t-distribution to construct a 98% 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:
The margin of error of mu is:
degrees of freedom = n - 1 = 18 - 1 = 17
t/2,df = t0.01,17 = 2.567
Margin of error = E = t/2,df * (s /n)
= 2.567 * ( 7.2 / 18)
Margin of error = E = 4.36
The 98% confidence interval estimate of the population mean is,
= 33.1 ± 4.36
= ( 28.74, 37.46 )
We are 98% confidence that the true mean commute time to work was between 28.74 and 37.46 minutes.
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