According to the American Association of Hematology, the proportion of blood phe

Question

According to the American Association of Hematology, the proportion of blood phenotypes for A, B, AB. and O in the population of all U.S. adults are 0.41,0.10, 0.04, and 0.45. respectively. A researcher at Penn State's Medical Center is interested in assessing whether the distribution for blood phenotypes for Penn State's undergraduate student body matches these U.S. rates. From Penn State's medical database. 200 undergraduates are randomly chosen resulting in 89 that are of Type A, 18 of Type B. 12 of Type AB, and the remaining 81 of Type O. he Goodness of Fit hypotheses to be tested using the above results are Hq : pH0.45 versus Ha: at least one probability P is not as listed in H0; where P is the proportion of all Penn State's undergraduates that are of Type A, P2 is the proportion of all Penn State's undergraduates that are of Type B, and so on f the null hypothesis is true, how many students in the random sample would be expected to fall in the Type A category he researcher conducting the test obtained an observed test statistic value of 3.7. Which of the following must be the corresponding p-value he observed test statistic of 3.7 is above the expected value for such a test statistic if the null hypothesis were true. About how many standard deviations above the expected value is it

Explanation / Answer

2.a.

There are n = 200 here, so

E(A) = n p1 = 200*0.41 = 82 [ANSWER]

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2.b

Here, k = 4 groups, so df = k - 1 = 3.

Hence, as chi^2 = 3.7, so using technology,

P = 0.296 [ANSWER, B]

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2.c

As

Mean = df = 3

standard deviation = sqrt(2 df) = sqrt(6) = 2.449489743

Then this is

(3.7-3)/2.449489743 = 0.285773803 = 0.29 standard deviations above the mean [ANSWER, A: 0.29]

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