In a random sample of 8 people, the mean commute time to work was 34.5 minutes a

Question

In a random sample of 8 people, the mean commute time to work was 34.5 minutes and the standard deviation was 7.3 minutes. A 90% confidence interval using the t-distribution was calculated to be (29.6,39.4). After researching commute times to work, it was found that the population standard deviation is 9.6 minutes. Find the margin of error and construct a 90% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results. The margin of error of (Round to two decimal places as needed.) A 90% confidence interval using the standard normal distribution is Round to one decimal place as needed.) Compare the results. Choose the correct ans: below A. The confidence interval found using the standard stribution its narrower than the confidence interval found using the s t-distribution. B. The confidence interval found using the standard normal distribution has smaller ower and upper confidence interval limits. confidence interval found using the standard normal distribution is the same as the confidence interval found using the student's t-distribution. The confidence interval found using the standard normal distribution is wider than the confidence interval found using the student's t-distribution 0 D. Cick to select your answer(s). 2 : 0 2 3 4 6 lab

Explanation / Answer

for std error =std deviation/(n)1/2 =9.6/(8)1/2 =3.394

for 90% CI ; crtiical value of z =1.6445

margin of error =z*Std error =5.58

therfore 90% confidence interval for mean =sample mean -/+ z*std error =28.9 to 40.1

option D is correct

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