Statistics

Question

Fewer young people are driving. In 1983, 87 percent of 19 year-olds had a driver's license. Twenty-five years later that percentage had dropped to 75 percent (University of Michigan Transportation Research Institute website, April 7, 2012). Suppose these results are based on a random sample of 1200 nineteen year-olds in 1983 and again in 2008.

a. At 95% confidence, what is the margin of error and the interval estimate of the number of nineteen year old drivers in 1983?

 

b. At 95% confidence, what is the margin of error and the interval estimate of the number of nineteen year old drivers in 2008?

 

c. is the margin of error the same in parts (a) and (b)? why or why not?

Answer 1

I'll get you started.

 

a. You can consider this to be a binomial distribution with n=1200 and p=.87

 

Using these values you can calculate  the interval for the "proportion"  by .87 ± z * σ where you calculate z based on the 95% value.

 

Multiply by 1200 to find the interval for the number of drivers in the sample.

 

The margin of error is 1200*z*σ .

 

b. Same techniques as a.

 

c. You can answer c after you get the erros in parts a and b.

 

 

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