Question

In a random sample of 25 people, the mean commute time to work was 32.9 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a t-distribution to construct a 98% confidence interval for the population mean μ: What is the margin of error of μ? Interpret the results. 

The confidence interval for the population mean μ is _______  

The margin of error of μ is _______ 

Interpret the results 

A. If a large sample of people are taken approximately 98% of them will have commute times between the bounds of the confidence interval 

B. It can be said that 98% of people have a commute time between the bounds of the confidence interval 

C. With 98% confidence, it can be said that the commute time is between the bounds of the confidence interval 

D. With 98% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 32.9

S = 7.1

n = 25

df = n – 1 = 24

Confidence level = 98%

Critical t value = 2.4922

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 32.9 ± 2.4922*7.1/sqrt(25)

Confidence interval = 32.9 ± 2.4922*1.42

Confidence interval = 32.9 ± 3.5389

Lower limit = 32.9 - 3.5389 =29.4

Upper limit = 32.9 + 3.5389 = 36.4

Confidence interval = (29.4, 36.4)

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

Margin of error = 2.4922*7.1/sqrt(25)

Margin of error =3.5389

Margin of error =3.5

Interpretation:

D. With 98% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.