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 6.2 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 sample size is greater than 30.
Because the sample size is less than 100.
Because the margin of error is less than 30.
Because the margin of error is positive.