Question

In a random sample of 22 ​people, the mean commute time to work was 32.1 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 μ. What is the margin of error of μ​? Interpret the results.

Answer 1

Solution :

Given that,

= 32.1

s = 7.3

n = 22

Degrees of freedom = df = n - 1 = 2 - 1 = 21

At1 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

_{t /2  df} = t_0.005,21 = 2.831

Margin of error = E = t_/2,df * (s /n)   

= 2.831 * (7.3/ 22) = 4.4060669

E=4.41 (rounded)