Question

In a random sample of 25 ​people, the mean commute time to work was 33.2 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a​ t-distribution to construct a 95​% confidence interval for the population mean muμ.

What is the margin of error of muμ​?

Interpret the results.

The confidence interval for the population mean

muμ

is (____,_______ )

​(Round to one decimal place as​ needed.)

The margin of error of

muμ 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 confidence interval.

B. If a large sample of people are taken approximately 95​% of them will have commute times between the bounds of the confidence interval.

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

D.It can be said that 95​%of people have a commute time between the bounds of the confidence interval.

Answer 1

Degrees of freedom (df) = n-1 = 25 - 1 = 24

t critical value at 0.05 significance level with 24 df = 2.064

95% confidence interval for is

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

33.2 - 2.064 * 7.1 / sqrt(25) < < 33.2 + 2.064 * 7.1 / sqrt(25)

30.3 < < 36.1

95% CI is ( 30.3 , 36.1)

Margin of error = t * S / sqrt(n)

= 2.064 * 7.1 / sqrt(25)

= 2.9

Interpretation -

With 95% confidence, it can be said that the population mean commute tie is between the

bounds of the confidence interval.