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.
a. What is the point estimate of the proportion of all Mustang coupe special orders that specify a color preference of black?
b. Describe the sampling distribution of , where 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.
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 will be between .31 and .41?

Question

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.  
a. What is the point estimate of the proportion of all Mustang coupe special orders that specify a color preference of black?
b. Describe the sampling distribution of  , where  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. 
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  will be between .31 and .41?

Quizplus · Accepted Answer

The Answer of 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.  
a. What is the point estimate of the proportion of all Mustang coupe special orders that specify a color preference of black?
b. Describe the sampling distribution of  , where  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. 
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  will be between .31 and .41?

Roger Hall, Who Oversees Six Ford Dealerships, Believes That the Colors