A 90% confidence interval for the number of hours that full-time college student

Question

A 90% confidence interval for the number of hours that full-time college students sleep during a weekday is lower bound: 7.8 hours and upper bound: 8.8 hours. Which of the following represents a reasonable interpretation of the result? For those that are not reasonable, explain the of flaw. (a) 90% of full-time college students sleep between 7.8 hours and 8.8 hours. (b) We are 90% confident that the mean number of hours of sleep that full-time college students get any day of the week is between 7.8 hours and 8.8 hours. (c) There is a 90% probability that the mean hours of sleep that full-time college students get during a weekday is between 7.8 hours and 8.8 hours. (d) We are 90% confident that the mean hours of sleep that full-time college students get during a weekday is between 7.8 hours and 8.8 hours.

Explanation / Answer

Option ( d ) represents a reasonable interpretation of the result .

Option ( d ) :

We are 90 % confident that the mean hours of sleep that full time college students get during a weekday is between 7.8 hours and 8.8 hours .

Option ( c ) is another interpretation of option ( d ) .

Flaws in other options :

Option ( a ) : The main flaw in option ( a ) is that it says that 90 % of full time college students sleep between 7.8 hours and 8.8 hours . Here the statement represents the proportion of full time college students who sleep between 7.8 hours and 8.8 hours . It doesnot represent an interval . Confidence interval is not a proportion .

Option ( b ) : The main flaw in option ( b ) is that it gives the 90 % confidence interval of the mean of the number of hours of sleep a full time college student gets in any day of the week . But actually we have the confidence interval of the number of hours of sleep a full time college student gets during a weekday .

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