An SRS of 500 motorcycle registrations finds that 68 of the motorcycles are Harl

Question

An SRS of 500 motorcycle registrations finds that 68 of the motorcycles are Harley-Davidsons.

Identify the 95 percent confidence interval for the proportion of all motorcycles that are Harleys by using the quick method.

A. 0.0913 to 0.1807

B. 0.1045 to 0.1554

C. 0.0776 to 0.1807 (wrong)

Step 2:

Identify the 95 percent confidence interval for the proportion of all motorcycles that are Harleys by using the more accurate method of this chapter:

A. 0.1038 to 0.1554

B. 0.1053 to 0.1667

C. 0.0774 to 0.1554 (wrong)

Explanation / Answer

a) here phat =68/500 =0.1360

and 1/(n)1/2 =0.0447

therefore confiednce interval =0.1360-/+ 0.447 =0.0913 to 0.1807 option A

steo 2)

std error of mean =(phat*(!-phat)/n)1/2 =0.0153

therfore confidence interval =0.1360-/+2*0.0153 =0.1053 to 0.1667

option B is correct

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