Question

In a random sample of 27 ​people, the mean commute time to work was 33.3 minutes and the standard deviation was 7.3 minutes. Assume the population is normally distributed and use a​ t-distribution to construct a 80​% 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 μ

(Round to one decimal place as​ needed.)

The margin of error of μ

​Round to one decimal place as​ needed.)

Int(erpret the results.

A.It can be said that

8080​%

of people have a commute time between the bounds of the confidence interval.

B.With

8080​%

​confidence, it can be said that the commute time is between the bounds of the confidence interval.

C.If a large sample of people are taken approximately

8080​%

of them will have commute times between the bounds of the confidence interval.

D.With

8080​%

​confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.

Answer 1

a)

t critical value at 0.20 significance level with 26 df = 1.315

80% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

33.3 - 1.315 * 7.3 / sqrt(27) < < 33.3 + 1.315 * 7.3 / sqrt(27)

31.5 < < 35.1

80% CI is ( 31.5 , 35.1 )

b)

Margin of error =  t * S / sqrt(n)

= 1.315 * 7.3 / sqrt(27)

= 1.8

c)

Interpretation -

With 80% confidence it can be said that the population mean commute time is between the bounds of the

confidence interval.