Question

In a random sample of 2121 ​people, the mean commute time to work was 30.130.1 minutes and the standard deviation was 7.17.1 minutes. assume the population is normally distributed and use a​ t-distribution to construct a 8080​% confidence interval for the population mean muμ. what is the margin of error of muμ​? interpret the results.

Answer 1

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.