The average student loan debt of a U.S. college student at the end of 4 years of college is estimated to be about $22,000. You take a random sample of 146 college students in the state of Vermont and find the mean debt is $23,000 with a standard deviation of $2,700. You want to construct a 90% confidence interval for the mean debt for all Vermont college students. (a) What is the point estimate for the mean debt of all Vermont college students? $ (b) Construct the 90% confidence interval for the mean debt of all Vermont college students. Round your answers to the nearest whole dollar. Write your answer in this format (lower limit, upper limit) (c) Are you 90% confident that the mean debt of all Vermont college students is greater than the quoted national average of $22,000 and why? Choose a, b, c, or d a. Yes, because $22,000 is above the lower limit of the confidence interval for Vermont students. b. No, because $22,000 is below the lower limit of the confidence interval for Vermont students. c. Yes, because $22,000 is below the lower limit of the confidence interval for Vermont students. d. No, because $22,000 is above the lower limit of the confidence interval for Vermont students. (d) We are never told whether or not the parent population is normally distributed. Why could we use the above method to find the confidence interval? Choose a, b, c, or d a. Because the margin of error is less than 30. b. Because the sample size is greater than 30. c. Because the margin of error is positive. d. Because the sample size is less than 100.
The average student loan debt of a U.S. college student at the end of 4 years of college is estimated to be about $22,000. You take a random sample of 146 college students in the state of Vermont and find the mean debt is $23,000 with a standard deviation of $2,700. You want to construct a 90% confidence interval for the mean debt for all Vermont college students. (a) What is the point estimate for the mean debt of all Vermont college students? $ (b) Construct the 90% confidence interval for the mean debt of all Vermont college students. Round your answers to the nearest whole dollar. Write your answer in this format (lower limit, upper limit) (c) Are you 90% confident that the mean debt of all Vermont college students is greater than the quoted national average of $22,000 and why? Choose a, b, c, or d a. Yes, because $22,000 is above the lower limit of the confidence interval for Vermont students. b. No, because $22,000 is below the lower limit of the confidence interval for Vermont students. c. Yes, because $22,000 is below the lower limit of the confidence interval for Vermont students. d. No, because $22,000 is above the lower limit of the confidence interval for Vermont students. (d) We are never told whether or not the parent population is normally distributed. Why could we use the above method to find the confidence interval? Choose a, b, c, or d a. Because the margin of error is less than 30. b. Because the sample size is greater than 30. c. Because the margin of error is positive. d. Because the sample size is less than 100.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Question 3 a,b,c,d
Transcribed Image Text:QUESTION 3
The average student loan debt of a U.S. college student at the end of 4 years of college is estimated to be about $22,000.
You take a random sample of 146 college students in the state of Vermont and find the mean debt is $23,000 with a
standard deviation of $2,700. You want to construct a 90% confidence interval for the mean debt for all Vermont college
students.
(a) What is the point estimate for the mean debt of all Vermont college students? $
(b) Construct the 90% confidence interval for the mean debt of all Vermont college students. Round your answers to the
nearest whole dollar. Write your answer in this format (lower limit, upper limit)
(c) Are you 90% confident that the mean debt of all Vermont college students is greater than the quoted national average of
$22,000 and why? Choose a, b, c, or d
a. Yes, because $22,000 is above the lower limit of the confidence interval for Vermont students.
b. No, because $22,000 is below the lower limit of the confidence interval for Vermont students.
c. Yes, because $22,000 is below the lower limit of the confidence interval for Vermont students.
d. No, because $22,000 is above the lower limit of the confidence interval for Vermont students.
(d) We are never told whether or not the parent population is normally distributed. Why could we use the above method to find
the confidence interval? Choose a, b, c, or d
a. Because the margin of error is less than 30.
b. Because the sample size greater than 30.
c. Because the margin of error is positive.
d. Because the sample size is less than 100.
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