Question

In: Statistics and Probability

The National Sleep Foundation (NSF) recommends that college students get between 8 and 9 hours of...

The National Sleep Foundation (NSF) recommends that college students get between 8 and 9 hours of sleep per night. Not believing this is happening at a local college, a random sample of 20 students resulted in a mean of 6.94 hours, with a standard deviation of 1.1 hours.

Part 1 of 3

If it is assumed that hours of sleep for college students is approximately normally distributed, construct and interpret a 95% confidence interval statement as well as a confidence level statement. Do the students at this local college meet the NSF recommendation? (Round your answers to two decimal places. Use a table or technology.

Solutions

Expert Solution

Given, mean = 6.94 hours,   standard deviation = 1.1 hours

Standard error of mean = = = 0.2459675

Degree of freedom, df = n-1 = 20 - 1 = 19

Critical value of t at 95% confidence interval and df = 19 is 2.093

95% confidence interval of hours of sleep for college students is,

(6.94 - 2.093 * 0.2459675, 6.94 + 2.093 * 0.2459675)

(6.43, 7.45)

Interpretation of 95% confidence interval statement - We're 95% confident that the interval (6.43, 7.45) captured the true mean hours of sleep per night for college students.

Interpretation of 95% confidence level statement - If we repeats this process many times, then about 95% of the intervals produced will capture the true mean hours of sleep per night for college students.

NSF recommends that college students get between 8 and 9 hours of sleep per night. Since the NSF recommendation range (8, 9) is outside the 95% confidence interval  (6.43, 7.45), the local college does not meet the NSF recommendation

orchestra answered 1 year ago
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