One thousand individuals were classified according to whether ornot they have a
ID: 2915546 • Letter: O
Question
One thousand individuals were classified according to whether ornot they have a particular genetic trait. The observed frequenciesare below
Men Women
HaveGene 442 514
Do not havegene 38 6
According to the genetic model these numbers should haverelative frequencies
Men Women
Havegene p/2 (p^2)/2 + pq
Do not havegene q/2 (q^2)/2
Where q=1-p and 0<p<1. Are the data consistent with themodel? Find the pvalue and make a decision at the 5% level ofsignificance.
Explanation / Answer
to find expected values, you have to find what p and qequal. so, (p/2)+(q/2)+((p^2)/2+pq)+((q^2)/2)=1000 and sinceq=1-p, (p/2)+((1-p)/2)+((p^2)/2+p(1-p))+(((1-p)^2)/2)=1000 solve for p. Then, to find the p-value, you have tofirst find the X2 values. For each section on the table, find((observed-expected)^2)/expected. Add all four valuestogether, and you'll have your X2 for your data. Now, you have to compare your X2 to a X2tail area table. Your table should have 2 axes (thisshould be in the back of your textbook). One axis is your-value (in your case 0.05) and the other axis is your degreesof freedom, or df. Since you have 4 categories,df=4-1=3. Find the spot on the table where your valuescross and that is your table X2 value. To find the p-value, go to the table in the back of the bookcorresponding to the Z tail areas and findP(Z>tableX2). if your value is greater than , do not reject your nullhypothesis (that data is represented by the model) if it is smaller, reject your null hypothesis. If you do not reject, this means that there is enoughstatistical evidence to confirm that your data supports themodel. If you do reject, it means that there is not enoughstatistical evidence to confirm that the data matches themodel.Related Questions
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