When public opinion surveys are conducted by mail, a cover letter explaining the purpose of the survey

Question:

When public opinion surveys are conducted by mail, a cover letter explaining the purpose of the survey is usually included. To determine whether the wording of the cover letter influences the response rate, three different cover letters were used in a survey of students at a Midwestern university (“The Effectiveness of Cover-Letter Appeals,” Journal of Social Psychology [1984]: 85–91). Suppose that each of the three cover letters accompanied questionnaires sent to an equal number of randomly selected students. Returned questionnaires were then classified according to the type of cover letter (I, II, or III). Use the accompanying data to test the hypothesis that π₁ = 1/3, π₂ = 1/3, and π₃ = 1/3, where π₁, π₂, and π₃ are the true proportions of all returned questionnaires accompanied by cover letters I, II, and III, respectively. Use a .05 significance level.