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 99 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.)

A. decrease z_α/2 by decreasing the confidence coefficient

B. increase z_α/2 by increasing the confidence coefficient

C. increase z_α/2 by decreasing the confidence coefficient

D. decrease the sample size nincrease the sample size n

E. decrease z_α/2 by increasing the confidence coefficient

F. conduct a non-random sample

Answer 1

we want to estimate the 95% confidence interval for proportion of sports utility vehicles in California

Let x = number of sports utility vehicles in California = 99

Given that

Confidence level = C = 0.95

sample size = n = 500

Therefor sample proportion is

95% confidence interval for population proportion is

Where,

Zc = Critical value for C =1.96 ..............( From Z table )

95% confidence interval for population proportion is

...................( ANSWER)

95% confidence interval for proportion of sports utility vehicles in California is

...........( ANSWER)

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B ) we can you estimate the proportion of sports utility vehicles in California with a higher degree of accuracy by

B )  increase zα/2 by increasing the confidence coefficient

D ) increase the sample size n

Option B and D are correct ...............( ANSWER )