Question 10.33

waterlootemp

33. High and low Temperatures. The University of Waterloo Weather Station tracks the daily low and high temperatures in Waterloo, Ontario, Canada. The table contains a random sample of the daily high and low temperatures in degrees Celsius for 10 days in calendar year 2010. Assume that the temperature differences are normally distributed.

Day 1 2 3 4 5 6 7 8 9 10
High 9.4 6.1 5.9 29.1 11.9 30.6 23.1 33.1 14.8 0.1
Low 0.8 −8.9 −1.3 19.3 6.7 21.5 10.5 18.7 7.4 −9.9
  1. Find the mean of the differences, , and the standard deviation of the differences, .
  2. Construct and interpret a 95% confidence interval for , the population mean difference in temperature.

10.1.33

Differences: 8.6, 15, 7.2, 9.8, 5.2, 9.1, 12.6, 14.4, 7.4, 10 (a) and (b) (7.6488, 12.211); We are 95% confident that the population mean of the differences between high and low temperatures in May in Waterloo, Ontario, Canada lies between 7.6488 degrees centigrade and 12.211 degrees centigrade.