Question

In a random sample of 18 ​people, the mean commute time to work was 34.7 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 μ. What is the margin of error of μ​? Interpret the results.

Answer 1

Given that,

n = 18

= 34.7   

s = 7.3  

Note that, Population standard deviation() is unknown..So we use t distribution.

Given , confidence interval = c = 80% = 0.80

= 1- c = 1- 0.80= 0.20

  /2 = 0.10

Also, d.f = n - 1 = 18 - 1 = 17

    =    =  _0.10,17 = 1.333

( use t table or t calculator to find this value..)

The margin of error is given by

E =  /2,d.f. * ( / n)

= 1.333 * (7.3 / 18)

= 2.2936

Margin of error = 2.2935

Interpretation: We are 80% confident that the population mean μ is within 2.2935 of the sample mean 34.7.