In a random sample of 29 people, the mean commute time to work was 34.4 minutes

Question

In a random sample of 29 people, the mean commute time to work was 34.4 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 . What is the margin of error of ? Interpret the results.

The confidence interval for the population mean is ( , )

(Round to one decimal place as needed.)

The margin of error of is ( , )

(Round to one decimal place as needed)

A.With 80% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.

B.With 80% confidence, it can be said that the commute time is between the bounds of the confidence interval.

C.If a large sample of people are taken approximately 80% of them will have commute times between the bounds of the confidence interval.

D.It can be said that 80% of people have a commute time between the bounds of the confidence interval.

Explanation / Answer

t value at 80% CI = 1.313
std.deviation = 7.3 , n = 29 , mean = 34.4

CI = mean + / - t * ( s / sqrt(n))
= 34.4 + /- 1.313 * ( 7.3 / sqrt(29))
= (32.6201 , 36.1798)

Margin of error = t * ( s /sqrt(n))
= 1.313 * ( 7.3 / sqrt(29))
= 1.7798

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