Question

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 50 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 t_α/2) for a 95% confidence interval? Use the value from the table or, if using software, round to 3 decimal places.
t_α/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 less than 100.

Because the margin of error is positive.    

Because the margin of error is less than 30.

Because the sample size is greater than 30.

Answer 1

This can be solved using excel<data<megastat<confiedence intervals:

Here is the output:

Confidence interval - mean
	95%	confidence level
	6.2	mean
	0.97	std. dev.
	50	n
	2.010	t (df = 49)
	0.276	margin of error
	5.924	lower confidence limit
	6.476	upper confidence limit

a) The point estimate for the mean nightly hours of sleep for all college students is the sample mean = 6.2

b) critical value =2.010

c) E= 0.28

d) 5.9 < μ <6.5

e) YES, because 7 is above the upper limit of the confidence interval for college students.

f) Because the sample size is greater than 30.

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