Global warming, Part II: Let's consider the differences between the temperature readings on January 1 of 1968 and 2008 at 51 locations in the continental US. The mean and standard deviation of the reported differences are 1.1 degrees and 4.9 degrees respectively. a) Calculate a 90% confidence interval for the average difference between the temperature measurements between 1968 and 2008. Round your answers to 2 decimal places. lower bound: degrees upper bound: degrees b) Interpret this interval in context. We are 90% confident that 90% of the time the differences in temperatures from year to year will be between the lower bound and upper bound We are 90% confident that the true mean difference in temperatures is contained between the lower bound and upper bound We are 90% confident that the mean difference in these sample temperatures is contained between the lower bound and upper bound There is a 90% chance that the difference in temperatures in a city from year to year will be between the lower bound and upper bound c) Does the confidence interval provide convincing evidence that the temperature was higher in 2008 than in 1968 in the continental US

Airplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. the indicated airspeed is the airspeed given by an instrument called an airspeed indicator. a plane’s indicated airspeed is different from its true airspeed because the indicator is affected by temperature changes and different altitudes of air pressure. the true airspeed is the speed of the airplane relative to the wind. ground speed is the speed of the airplane relative to the ground. for example, a plane flying at a true airspeed of 150 knots into a headwind of 25 knots will have a ground speed of 125 knots. the problems below refer to static and dynamic pressure. static pressure is used when a body is in motion or at rest at a constant speed and direction. dynamic pressure is used when a body in motion changes speed or direction or both. a gauge compares these pressures, giving pilots an indicated airspeed. in problem #s 1 and 2, use the following information. the indicated airspeed s (in knots) of an airplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures. the relationship between s and p can be modeled by s=136.4p√+4.5. 1. find the differential pressure when the indicated airspeed is 157 knots. 2. find the change in the differential pressure of an airplane that was traveling at 218 knots and slowed down to195 knots. in problem #s 3 and 4, use the following information. the true airspeed t (in knots) of an airplane can be modeled by t=(1+a50,000) ⋅ s, where a is the altitude (in feet) and s is the indicated airspeed (in knots). 3. write the equation for true airspeed t in terms of altitude and differential pressure p. 4. a plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. estimate the differential pressure. explain why you think your estimate is correct.