This Question: 3 pts 16 of 19 (10 complete) his cu: 60 pis possl in a random sam

Question

This Question: 3 pts 16 of 19 (10 complete) his cu: 60 pis possl in a random sample of 24 people, the mean commute time to work was 33.5 minutes a 1-0 stribution to construct a 99% confidence interval for the population mean whats the margin of error of ? Interpret the and the standard deviation was 7 2 minutes Assume the population is normaly distrbuted and use results The confidence interval for the population mean is UD (Round to one decimal place as needed ) The margin of error of (Round to one decimal place as needed) Interpret the results OA. itcan be said that 99% of poople have a commate trne between the bounds of the confidence interval B. C. OD. with 99% confidence· it can be sad that the populabon rman commute tne s between the bounds of the cotdence noval " a large sample of people are taken approximately 90% of them wil have corrmto tmes betwoon the tourds ofthe cont once rtemi With 99% confidence. it can be said that the commite time is between the bounds ofthe confidence interval

Explanation / Answer

N = 24 people

Mean commute time = 33.5

SD = 7.2 minutes

99% CI = mean ± margin of error

Margin of error = critical point value for level of confidence X standard error

Critical value for 99% CI for t statistics = 2.8073

Standard error = 7.2/24 = 7.2/4.8989 = 1.4697

Margin of error = 2.8073 X 1.4697 = 4.12

99% CI = 33.5 ± 4.12

Therefore, lower limit of 99% CI = 29.38

Upper limit of 99% CI = 37.62

Analysis conducted in STATA software for the same also observed the same results. The output is given below.

cii 24 33.5 7.2, level(99)

Variable | Obs Mean Std. Err. [99% Conf. Interval]
-------------+---------------------------------------------------------------
| 24 33.5 1.469694 29.38 37.62592

Margin of error = 4.12

Interpret the results

The correct answer is B. (With 99% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.