Sleep – College Students: Suppose you perform a study about the hours of sleep t

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Sleep – College Students: Suppose you perform a study about the hours of sleep that college students get. You know that for all people, the average is about 7 hours. You randomly select 45 college students and survey them on their sleep habits. From this sample, the mean number of hours of sleep is found to be 6.1 hours with a standard deviation of 0.86 hours. You want to construct a 99% confidence interval for the mean nightly hours of sleep for all college students. (a) What is the point estimate for the mean nightly hours of sleep for all college students? hours (b) Construct the 99% confidence interval for the mean nightly hours of sleep for all college students. Round your answers to 1 decimal place. < < (c) Are you 99% confident that the mean nightly hours of sleep for all college students is below the average for all people of 7 hours per night? Why or why not? Yes, because 7 is above the upper limit of the confidence interval for college students. No, because 7 is below the upper limit of the confidence interval for college students. Yes, because 7 is below the upper limit of the confidence interval for college students. No, because 7 is above the upper limit of the confidence interval for college 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? Because the sample size is greater than 30. Because the margin of error is positive. Because the sample size is less than 100. Because the margin of error is less than 30. Additional Materials eBook 9.–/1 points 0/4 Submissions Used StevensStat4 7.P.009.Data. My Notes Question Part Points Student Debt – Vermont (Raw Data, Software Required): The average student loan debt of a U.S. college student at the end of 4 years of college is estimated to be about $22,700. You take a random sample of 40 college students in the state of Vermont. The debt for these students is found in the table below. We want to construct a 95% confidence interval for the mean debt for all Vermont college students. You will need software to answer these questions. You should be able to copy and paste the data directly from the table into your software program. (a) What is the point estimate for the mean debt of all Vermont college students? Round your answers to the nearest whole dollar. $ (b) Construct the 95% confidence interval for the mean debt of all Vermont college students. Round your answers to the nearest whole dollar. < < (c) Are you 95% confident that the mean debt of all Vermont college students is greater than the quoted national average of $22,700 and why? No, because $22,700 is below the lower limit of the confidence interval for Vermont students. Yes, because $22,700 is below the lower limit of the confidence interval for Vermont students. Yes, because $22,700 is above the lower limit of the confidence interval for Vermont students. No, because $22,700 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? Because the margin of error is positive. Because the sample size is greater than 30. Because the sample size is less than 100. Because the margin of error is less than 30.

Student Debt    1 22406 2 26436 3 24322 4 25293 5 21767 6 25039 7 27408 8 25421 9 25245 10 21071 11 24377 12 24271 13 19344 14 22566 15 23742 16 24251 17 22123 18 26683 19 25574 20 19372 21 19607 22 27085 23 22236 24 25239 25 26700 26 21424 27 23140 28 22930 29 23869 30 23879 31 23641 32 26625 33 23193 34 23816 35 24887 36 26439 37 21463 38 22878 39 28504 40 25578

Explanation / Answer

a)   the point estimate for the mean nightly hours of sleep for all college students is sample mean = 6.1

b)

n = 45, xbar = 6.1 , s = 0.86

99 % confidence interval

t-critical for 99 % confidence level is 2.692

is (Xbar -t* s/sqrt(n)) , (Xbar + t* s/sqrt(n))

(6.1 - 2.692*0.86/sqrt(45)),6.1 + 2.692*0.86/sqrt(45)),

(5.754882286, 6.4451177)

c) we are 99% confident that the mean nightly hours of sleep for all college students is below the average for all people of 7 hours per night

option A) Yes, because 7 is above the upper limit of the confidence interval for college students. is correct

we use the above method to find the confidence interval

Because the sample size is greater than 30. is correct

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