The report referenced in the previous exercise also gave data for representative samples of 250 adults in Canada and in England. The sample mean amount of sleep on a work night was 423 minutes for Canada and 409 minutes for England. Suppose that the sample standard deviations were 35 minutes for the Canada sample and 42 minutes for the England sample.

a. Construct and interpret a 95% confidence interval estimate of the difference in the mean amount of sleep on a work night for adults in Canada and adults in England.

b. Based on the confidence interval from Part (a), would you conclude that there is evidence of a difference in the mean amount of sleep on a work night for the two countries? Explain why or why not.

Previous exercise

The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about sleeping habits (“2013 International Bedroom Poll Summary of Findings,” sleepfoundation.org/sites/default/files/RPT495a .pdf). Each person in a representative sample of 250 adults in each of these countries was asked how much sleep they get on a typical work night. For the United States, the sample mean was 391 minutes and for Mexico the sample mean was 426 minutes. Suppose that the sample standard deviations were 30 minutes for the U.S. sample and 40 minutes for the Mexico sample. The report concludes that on average, adults in the United States get less sleep on work nights than adults in Mexico. Is this a reasonable conclusion? Support your answer with an appropriate hypothesis test.