aragraph Styles 129. Roger Hall, who oversees six Ford dealerships, believes tha
ID: 3371476 • Letter: A
Question
aragraph Styles 129. Roger Hall, who oversees six Ford dealerships, believes that the colors chosen by customers who special-order their cars best reflect most customers' true color preferences. For that reason, he has tabulated the color requests specified in a sample of 56 Mustang coupe special orders placed this year. The sample data are listed below. Black Red White ue Blue Green Red Black Red White Blue White Red Red Black Black Green Black Red Black Blue Black White Green Blue Red Black White Black Red Black Blue Blue Black Green White Black Red Red White Red Red Blue Black Red Black Green Black Green Red Black White Black Red Black White a. What is the point estimate of the proportion of all Mustang coupe special orders that specify a color preference of black? Answer b. Describe the sampling distribution of F, where P is the proportion of Mustang coupe special orders that specify a color preference of black Assume that the proportion of all Mustang coupe special orders having a color preference of black is 36. Answer: c. What is the probability that a simple random sample of 56 special orders will provide an estimate of the population proportion of special orders specifying the color black that is within plus or minus 05 of the actual population proportion, assuming p 36? In other words, what is the probability that P will be between 31 and .41?Explanation / Answer
Result:
n=56
With black = 18
Proportion p= 18/56 =0.3214
b).
sampling distribution with mean =0.36
and with standard deviation sqrt(p(1-p)/n) = sqrt(0.36*(1-0.36)/56) =0.0641
c).
z value for 0.31, z = (0.31-0.36)/0.0641 = -0.78
z value for 0.41, z = (0.41-0.36)/0.0641 = 0.78
P( 0.31<P<0.41) = P( -0.78 < z < 0.78)
= P( z < 0.78) – P( z < -0.78)
=0.7823 -0.2177
=0.5646
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