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 0.86 hours. we want to construct a 95% confidence interval for the mean nightly hours of sleep for all college students, what is the point estimate for the mean nightly hours of sleep for all college students?

With 95% confidence, mean nightly hours of sleep for all college student is between 5,9616 and 6,4384 hours.

Explanation:

Sample mean of sleeping hours of randomly selected 50 college students deviates from the mean of sleeping hours of all college students. We need to calculate margin of error for the sample mean to make an estimate for all college students.

The general formula for the margin of error for the sample mean is

where z is the appropriate z-value for your desired level of confidence (for 95% it is approximately 1.96), s is the sample standard deviation (in fact it is population standard deviation but it is replaced when this value is unknown), and N is the sample size.

Then our formula becomes which is equal to 0.2383798

As a result, with 95% confidence, hours of sleep of all college students in average is between 6.2-0.2383798 and 6.2+0.2383798, ie between  5,9616 and 6,4384 hours.

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