A sample survey is designed to estimate the proportion of sports utility vehicle

Question

A sample survey is designed to estimate the proportion of sports utility vehicles being driven in the state of California. A random sample of 500 registrations are selected from a Department of Motor Vehicles database, and 26 are classified as sports utility vehicles.

(a) Use a 95% confidence interval to estimate the proportion of sports utility vehicles in California. (Round your answers to three decimal places.) ______ to _______

(b) How can you estimate the proportion of sports utility vehicles in California with a higher degree of accuracy? (HINT: There are two answers. Select all that apply.)

decrease z?/2 by decreasing the confidence coefficient

increase the sample size n

increase z?/2 by decreasing the confidence coefficient

decrease the sample size n

conduct a non-random sample

decrease z?/2 by increasing the confidence coefficient

increase z?/2 by increasing the confidence coefficient

You may need to use the appropriate appendix table or technology to answer this question.

Explanation / Answer

Solution:- Given that n = 500 , x = 26

p = 26/500 = 0.052 , q = 1-p = q = 0.948

(a) 95% confidence interval for the proportion of sports utility vehicles in california : p +/- Z*sqrt(pq/n)
: 0.052 +/- 1.96*sqrt(0.052*0.948/500)
: 0.033 , 0.071

(b) => increase z?/2 by increasing the confidence coefficient

=>  decrease z?/2 by decreasing the confidence coefficient
  

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