The National Sleep Foundation surveyed representative samples ofadults in six different countries to ask questions about sleepinghabits.†Each person in a representative sample of 250 adults ineach of these countries was asked how much sleep they get on atypical work night. For the United States, the sample mean was 391minutes, and for Mexico, the sample mean was 426 minutes.
The report also gave data for representative samples of 250adults in Canada and in England. The sample mean amount of sleep ona work night was 423 minutes for Canada and 409 minutes forEngland. Suppose that the sample standard deviations were 35minutes for the Canada sample and 41 minutes for the Englandsample.
(a)
Construct a 95% confidence interval estimate of the differencein the mean amount of sleep (in minutes) on a work night for adultsin Canada and adults in England. (Use
μCanada − μEngland.
Round your answers to three decimal places.)
,
minutes
Interpret the interval.
We are 95% confident that the difference in the mean amount ofsleep on a work night for the adults studied in Canada and Englandfalls within this interval.There is a 95% chance that thedifference in the mean amount of sleep on a work night for adultsin Canada and adults in England falls directly in the middle ofthis interval.    There is a 95% chance thatthe true difference in the mean amount of sleep on a work night foradults in Canada and adults in England falls directly in the middleof this interval.There is a 95% chance that the difference in themean amount of sleep on a work night for adults in Canada andadults in England falls within this interval.We are 95% confidentthat the true difference in the mean amount of sleep on a worknight for adults in Canada and adults in England falls within thisinterval.
(b)
Based on the confidence interval from part (a), would youconclude that there is evidence of a difference in the mean amountof sleep on a work night for the two countries? Explain why or whynot.
The confidence interval  ---Select--- (does not allowus/allows us to) conclude that there is evidence of a difference inthe mean amount of sleep on a work night for the two countriesbecause zero  ---Select--- (is not,is) contained in theconfidence interval.
