Question: In an experiment conducted by one of the authors, ten students in a graduate-level statistics course were given this question about the population of Canada: "The population of the U.S. is about 270 million. To the nearest million, what do you think is the population of Canada?" (The population of Canada at the time was slightly over 30 million.) The responses (in millions) were as follows:
20, 90, 1.5, 100, 132, 150, 130, 40, 200, 20
Eleven other students in the same class were given the same question with different introductory information: "The population of Australia is about 18 million. To the nearest million, what do you think is the population of Canada?" The responses (in millions) were as follows:
12, 20, 10, 81, 15, 20, 30, 20, 9, 10, 20
The experiment was done to demonstrate the anchoring effect, which is that responses to a survey question may be "anchored" to information provided to introduce the question. In this experiment, the research hypothesis was that the individuals who saw the U.S. population figure would generally give higher estimates of Canada's population than would the individuals who saw the Australian population figure.
a. Write null and alternative hypotheses for this experiment. Use proper notation.
b. Test the hypotheses stated in part (a). Be sure to state a conclusion in the context of the experiment. Specify the value of a that you chose to use.
c. As a step in part (b), you should have created a graphical summary to verify necessary conditions. Do you think that any possible violations of the necessary conditions have affected the results of part (b) in a way that produced a misleading conclusion? Explain why or why not.