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EXERCISE

EXERCISE. ANOVA & CATEGORICAL DATA. Exercise 1. A partially completed ANOVA table for a completely randomized design is shown here: Complete the ANOVA table How many blocks and treatments were used in the experiment? How many observations were collected in the experiment?

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EXERCISE

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  1. EXERCISE ANOVA & CATEGORICAL DATA

  2. Exercise 1 • A partially completed ANOVA table for a completely randomized design is shown here: • Complete the ANOVA table • How many blocks and treatments were used in the experiment? • How many observations were collected in the experiment? • Specify the null and alternative hypotheses you would use to compare the treatment means. • What test statistics should be used to conduct the hypotheses test in part d. • Specify the rejection region for the test of parts d and e. Use  = .01 Source SS df MS F Treatment 501 4 Block 2 Error 110 Total 836 14

  3. Answer Source SS df MS F Treatment 501 4 125.25 8.18 Block 225 2 115.5 9.11 Error 110 813.75 Total 836 14 a) b) 3 blocks and 5 treatment c) 15 observations d) For treatment: Ho: 1 = 2 = 3 = 4 = 5 Ha: At least on of the treatment means is different For blocking: Ho: 1 = 2 = 3 Ha: At least on of the blocking means is different e) F statistics f) Treatment ; Critical F = F0.01,4,8 = 7.01 Calculation F = 9.11 ; Fcritical = 7.01 < F cal = 9.11, reject H0 Blocking ; Critical F = F0.01,2,8 = 8.65 Calculation F = 8.182 ; Fcritical = 8.65 > F cal = 8.182, fail to reject H0

  4. Exercise 2 • A large brokerage firm wants to determine whether the service it provides to affluent clients differ from the service it provides to lower income clients. A sample of 500 clients are selected, and each client is asked to rate his or her broker. The results are shown in Table below. Test to determine whether there is evidence that broker rating and customer income are independent. Use =.10

  5. Answer

  6. Answer (cont..) Ho: The rating client gives his or her broker is independent of client’s income Ha: Broker rating and client income are dependent Critical 2 = 20.01,4 = 7.7794  (fo-fe)2/fe = 4.277 2 calculation < 2 critical, fail to reject Ho

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