Jennifer wants to find a 95% confidence interval for the time it takes her to get to work. She kept records
for 30 days and found her average time to commute to work was 20.5 minutes with a standard deviation
of 3.9 minutes. Jennifer's maximum error of estimate would be 1.4 minutes.

Question

Quizplus · Accepted Answer

To find the confidence interval, we can use the formula:

CI = x̄ ± z*(σ/√n)

where x̄ is the sample mean (20.5), σ is the sample standard deviation (3.9), n is the sample size (30), and z is the critical value from the standard normal distribution for a 95% confidence level (which is approximately 1.96).

Plugging in the values, we get:

CI = 20.5 ± 1.96*(3.9/√30)
   = 20.5 ± 1.39

This means that we are 95% confident that Jennifer's true commute time falls within the range of 19.11 to 21.89 minutes. Since the maximum error of estimate given is 1.4 minutes, and the actual range of the confidence interval is within 1.39 minutes, the statement is true.

Jennifer Wants to Find a 95% Confidence Interval for the Time