The earth's temperature can be measured using either ground-based sensors or infrared-sensing devices mounted in aircraft or space satellites. Ground-based sensoring is very accurate but tedious, while infrared-sensoring appears to introduce a bias into the temperature readings-that is, the average temperature reading may not be equal to the average obtained by ground-based sensoring. To determine the bias, readings were obtained at five different locations using both ground- and air-based temperature sensors. The readings (in degrees Celsius) are listed here:

a. Do the data present sufficient evidence to indicate a bias in the air-based temperature readings? Explain.
b. Estimate the difference in mean temperatures between ground- and air-based sensors using a 95% confidence interval.
c. How many paired observations are required to estimate the difference between mean temperatures for ground- versus air-based sensors correct to within .2°C, with probability approximately equal to .95?

Location Ground Air 46.9 47.3 45.4 48.1 36.3 37.9 31.0 32.7 24.7 262