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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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