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 35 college students and survey them on their sleep habits. From this sample, the mean number of hours of sleep is found to be 6.2 hours with a standard deviation of 0.97 hours. We want to construct a 95% 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) What is the critical value of t (denoted
tα/2) for a 95% confidence interval?
Use the value from the table or, if using software, round
to 3 decimal places.
tα/2 =
(c) What is the margin of error (E) for a 95% confidence
interval? Round your answer to 2 decimal
places.
E = hours
(d) Construct the 95% confidence interval for the mean nightly
hours of sleep for all college students. Round your answers
to 1 decimal place.
< μ <
(e) Based on your answer to (d), are you 95% 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.
(f) 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 margin of error is less than 30.
Because the sample size is greater than 30.
Because the sample size is less than 100.
Solution:- Given that mean = 6.2, standard deviation = 0.97, n = 35
(a) point estimate for the mean = 6.2
(b) df = n-1 = 35-1 =34
tα/2 = 2.032
(c) margin of error(E) = t*s/sqrt(n) = 2.032*0.97/sqrt(35) = 0.33
(d) 95% confidence interval : X +/- ME =
: 6.2 +/- 0.33
: 5.87 , 6.55
(e) option A.Yes, because 7 is above the upper limit of the confidence interval for college students
(f) option C. Because the sample size is greater than 30.
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