Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (°F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y = 5.00 - .01x and ( = .075.
a. What is the expected change in reaction time for a 1°F increase in temperature? For a 10°F increase in temperature?
b. What is the expected reaction time when temperature is 200°F? When temperature is 250°F?
c. Suppose five observations are made independently on reaction time, each one for a temperature of 250°F. What is the probability that all five times are between 2.4 and 2.6 hr?
d. What is the probability that two independently observed reaction times for temperatures 1° apart are such that the time at the higher temperature exceeds the time at the lower temperature?