Question

In a random sample of 26 ​people, the mean commute time to work was 30.7 minutes and the standard deviation was 7.2 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 mu is(-,-) ​(Round to one decimal place)

The margin of error of mu is___. ​(Round to one decimal place)

Interpret the results

.A. If a large sample of people are taken approximately 80​% of them will have commute times between the bounds of the confidence interval.

B. It can be said that 80​% of people have a commute time between the bounds of the confidence interval.

C. With 80​% ​confidence, it can be said that the population mean commute time is between the bounds of the confidence interval

D. With 80​% ​confidence, it can be said that the commute time is between the bounds of the confidence interval.  

Answer 1

Solution:

Given:

Sample Size = n = 26

Sample mean =

Sample Standard Deviation = s = 7.2

We have to  use a​ t-distribution to construct a 80​% confidence interval for the population mean .

Formula:

where

t_c is t critical value for c = 80%  confidence level

Thus two tail area = 1 - c = 1 - 0.80= 0.20

df = n - 1 =  26- 1 = 25
Look in  t table for df =25 and two tail area = 0.20 and find t critical value

t_c= 1.316

thus

Thus Margin of Error =

Thus

The confidence interval for the population mean is:

Interpret the results

C. With 80​% ​confidence, it can be said that the population mean commute time is between the bounds of the confidence interval

We construct confidence interval for population parameter like population mean, population proportion etc,thus interpretation should be about population mean. Thus option C is correct.