A certain geneticist is interested in the proportion of males and females in the
ID: 3126364 • Letter: A
Question
A certain geneticist is interested in the proportion of males and females in the population who have a minor blood disorder. In a random sample of 1000 males 250 are found to be afflicted, whereas 275 of 1000 females tested appear to have the disorder. Compute a 95% CI for the difference between the proportions of males and females who have the blood disorder. The federal government awarded grants to the agricultural departments of 9 universities to test the yield capabilities of two new varieties of wheat. Each variety was planted on a plot of equal area at each university, and the yields, in kilograms per lot, were recorded as follows: Find a 95% CI for the mean difference between the yields of the two varieties, assuming the differences of the yields to be approximately normally distributed. Explain why pairing is necessary in this problem.Explanation / Answer
Calculating the standard deviation of the differences :
s = 4.100073909
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 1.366691303
Calculating the mean of the differences
XD = 2.777777778
For the 0.95 confidence level,
alpha/2 = (1 - confidence level)/2 = 0.025
Z(alpha/2) = 1.959963985
lower bound = [X1 - X2] - Z(alpha/2) * sD = 0.099112046
upper bound = [X1 - X2] + Z(alpha/2) * sD = 5.45644351
Thus, the confidence interval is
( 0.099112046 , 5.45644351 ) [ANSWER]
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Pairing is necessary becasue each university had 2 varieties, so there's natural pairing between the data points.
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