Question: Refer to Exercise, part (a), which posed the following research question: "Many cars have a recommended tire pressure of 32 psi (pounds per square inch). At a roadside vehicle safety checkpoint, officials plan to randomly select 50 cars for which this is the recommended tire pressure and measure the actual tire pressure in the front left tire. They want to know whether drivers on average have too little pressure in their tires." Suppose that the experiment is conducted, and the mean and standard deviation for the 50 cars tested are 30.1 psi and 3 psi, respectively. Carry out the five steps to test the appropriate hypotheses using a = .05. (Use a p-value, not a rejection region.)
Exercise: Define the parameter of interest, and then use it to write the null and alternative hypotheses (in symbols) for each of the following research questions.
a. Many cars have a recommended tire pressure of 32 psi (pounds per square inch). At a roadside vehicle safety checkpoint, officials plan to randomly select 50 cars for which this is the recommended tire pressure and measure the actual tire pressure in the front left tire. They want to know whether drivers on average have too little pressure in their tires.
b. The box of Yvette's favorite cereal states that the net contents weigh 12 ounces. Yvette is suspicious of this claim because the package never seems full to her. She plans to measure the weight of the contents of the next 20 boxes she buys and find out whether she is being short-changed.