A government executive in a large city had recently read an article that stated
ID: 3320899 • Letter: A
Question
A government executive in a large city had recently read an article that stated people in his city had an average commute time of 24 minutes per day. The executive thought the actual time was more than this. To examine this question he surveyed a random sample of 87 employees working in the city and recorded their commute time. The resutling data was used to create this output.
Which of the following would be closest to a 95% confidence interval for the sample mean?
a. (88.10, 91.02)
b. (32.04, 38.96)
c. (28.92, 35.08)
d. (33.25, 37.75)
I know the answer is b. but I don't know why. Can you please explain?
Variable Sample Mean Std. Err. DF T-Stat P-value Commute Time 35.5 1.74 86 xxxx <0.0001Explanation / Answer
Given,
Degrees of freedom = 86
For 86 degrees of freedom and 95% confidence interval,
Critical t value = 1.988
From the table,
Sample mean = 35.5
Standard error = 1.74
Hence,
95% confidence interval will be:
(35.5 - 1.988*1.74, 35.5 + 1.988*1.74)
(32.04, 38.96)
Option B is correct.
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