The margin of error can be calculated using the t statistic. The formula for margin of error is given as:
Margin of error = t * s / sqrt (n) ---> 1
Where,
t = the t score based on the given confidence level and degrees of freedom
n = number of samples = 21
s = standard deviation = 7.1
Degrees of freedom = n – 1 = 21 – 1 = 20
Based on the standard probability tables for t, the t score is:
t = 0.860
Substituting into equation 1:
margin of error = 0.860 * 7.1 / sqrt (21)
margin of error = 1.33
The range is:
range = 30.1 ± 1.33
range = 28.77, 31.43
Therefore the commute time to work is between 28.77 minutes and 31.43 minutes.
