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

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. 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 hypothecs that pi _1 = 1/3, pi _2 = 1/3, and pi _3 = 1/3, where pi _1, pi _2 and pi _3 are the true proportions of all returned questionnaires accompanied by cover letters I, II, and III, respectively. Use a 0.05 significance level. (Use 2 decimal places.) chi ^2 = P-value interval p

Explanation / Answer

Answer:

Goodness of Fit Test

observed

expected

O - E

(O - E)² / E

51

40.667

10.333

2.626

37

40.667

-3.667

0.331

34

40.667

-6.667

1.093

Total

122

122.000

4.049

4.05

chi-square

2

df

.1320

p-value

Chi square = 4.05

P value   p ? 0.10

Conclusion

Ho is not rejected.

Goodness of Fit Test

observed

expected

O - E

(O - E)² / E

51

40.667

10.333

2.626

37

40.667

-3.667

0.331

34

40.667

-6.667

1.093

Total

122

122.000

4.049

4.05

chi-square

2

df

.1320

p-value

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