Question

Historically, the proportions of all Caucasians in the United States with blood phenotypes A, B, AB, and O are 0.41, 0.10, 0.04, and 0.45, respectively. To determine whether current population proportions still match these historical values, a random sample of 200 American Caucasians were selected, and their blood phenotypes were recorded. The observed numbers with each phenotype are given in the following table. 8817 13 2 (a) Is there sufficient evidence, at the 0.05 level of significance, to claim that current proportions differ from the historic values? State the null and alternative hypotheses. (Use P P P o for the proportions of Caucasions in the United States with phenotypes A, B, AB, and O respectively.) O Ho: the proportions differ from this sample Ha: PA-0.44, P-0.09,PA-0.0, Po- 0.41 Ha: the proportions differ from this sample Ha: PA-0.41. P-Q10, PA-0.04, Po-0.45 Ha: the proportions are not all equal Ha: the propro tions differ from the historical values Ho: PA-044, P0.0, PA-0.07, Po-4 O Ho: the proportions differ from the historical values OHo: PA-02, P-0.25, PA-0.25, Po-025 O Ho:A-041, Pa-0.10, PA-0.04, Po-0.45 Calculate the test statistic. (Round your answer to three decimal places.) State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) What is the conclusion of your test? O Reject Hor There is sufficient evidence to to claim that current proportions O Fail to reject o There is sufficient evidence to claim that current O Fail to reject Hor There is not sufficient evidence to claim that current O Reject o There is not sufficient evidence to claim that current differ from the historic values. proportions differ from the historic values. proportions differ from the historic values. proportions differ from the historic values. ) Use technology to find the p-value associated with the test in part (a). (Round your answer to three decimal places.) -value You may need to use the appropriate appendix table or technology to answer

Answer 1

Ho: p-0.41, p 0.10, puB-0.04, Po 0.45 Ha: the proportions differ from the historical values Observed values Expected values 200(0.41) 82 200(0.10) 20 200 (0.04) 8 200 (0.45) 90 Sample 17 13 82 AB EXCEL Mega Stat) output: Goodness of Fit Test O -E 6.000 3.000 5.000 8.000 0.000 EP/E 0.439 0.450 3.125 %ofchis observed expected 82.000 20.000 8.000 90.000 200.000 9.29 9.52 66.14 15.05 100.00 17 13 82 200 4.725 4.73 chi-square 3 df 1931 p-value

The value of test statistic is X2-4725 Rejection region: 7.815 Fail to reject Ho There is not sufficient evidence to cliam that current proportions differ from the hostoric values (b) p-value = 0.193.