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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 (denoted ) for a 95% confidence interval? = (c) What is the margin of error ( ) for a 95% confidence interval? =  hours (d) Construct the 95% confidence interval for the mean nightly hours of sleep for all college students. < < (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? (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?

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

You are studying the affect of financial means on students' average hours of sleep. You have found a reliable study indicating that students that have a job and do not receive financial support from their parents or guardians sleep an average of 5.8 hours per night (excluding weekends) on average (population average).
You decide to test whether or not students who do not work get more sleep per week night on average. You take a sample of 63 students that do not work and live with parents or guardians then you record the number of hours per week night they sleep for a period of 15 weeks (1 semester). You find that the average (mean) hours slept per week night in your sample is 7.2 hours and the standard deviation is 3.9 hours. Assume that average sleeping hours on week nights is normally distributed across students.
 
Remember to define the null and alternative hypotheses to help you answer the question.
 
What will the value of the test statistic (z-test) be?
(Round your answer to two decimal places)

After surveying students at Dartmouth College, a campus organization calculated that a 95% confidence interval for the mean cost of food for one term (of three in the Dartmouth trimester calendar) is ($1372, $1562). Now the organization is trying to write its report and is considering the following interpretations. Comment on each.

a) 95% of all students pay between $1372 and $1562 for food.

b) 95% of the sampled students paid between $1372 and $1562.

c) We're 95% sure that students in this sample averaged between $1372 and $1562 for food.

d) 95% of all samples of students will have average food costs between $1372 and $1562.

e) We're 95% sure that the average amount all students pay is between $1372 and $1562.

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