Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

In a random sample of 8 ​people, the mean commute time to work was 35.5 minutes and the standard deviation was 7.4 minutes. A 90​% confidence interval using the​ t-distribution was calculated to be (30.5,40.5). After researching commute times to​ work, it was found that the population standard deviation is 9.3 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.

Sagot :

fichoh

Answer:

Margin of Error = 5.4088 ;

Confidence interval = (30.1 ; 40.9)

Interval estimate are almost the same

Step-by-step explanation:

Given that :

Population standard deviation, σ = 9.3

Sample size, n = 8

Xbar = 35.5

Confidence level = 90%

The confidence interval:

Xbar ± Margin of error

Margin of Error = Zcritical * σ/sqrt(n)

Zcritical at 90% = 1.645

Margin of Error = 1.645 * 9.3/sqrt(8) = 5.4088

Confidence interval :

Xbar ± Margin of error

35.5 ± 5.4088

Lower boundary = (35.5 - 5.4088) = 30.0912 = 30.1

Upper boundary = (35.5 + 5.4088) = 40.9088 = 40.9

(30.1 ; 40.9)

T distribution =. (30.5 ; 40.5)

Normal distribution = (30.1, 40.9)

Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.