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In a random sample of 19 ​people, the mean commute time to work was 30.7 minutes and the standard deviation was 7.3 minutes. Assume the population is normally distributed and use a​ t-distribution to construct a 99​% confidence interval for the population mean mu. What is the margin of error of mu​? Interpret the results.

Answer :

princessesther2011

Answer:

The margin of error of mu is 4.82 minutes

99% confidence interval for mu is between a lower limit of 25.88 minutes and an upper limit of 35.52 minutes

Step-by-step explanation:

Margin of error (E) = t × sd/√n

population mean (mu) = 30.7 minutes

sd = 7.3 minutes

n = 19

degree of freedom = n - 1 = 19 - 1 = 18

confidence level = 99%

t-value corresponding to 18 degrees of freedom and 99% confidence level is 2.878

E = 2.878 × 7.3/√19 = 4.82 minutes

Lower limit = mu - E = 30.7 - 4.82 = 25.88 minutes

Upper limit = mu + E = 30.7 + 4.82 = 35.52 minutes

99% confidence interval for the mean commute time to work is between 25.88 and 35.52 minutes.

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