Fewer young people are driving. In year A, 61.9% of people under 20 years old who were eligible had a driver's license. Twenty years later in year B that percentage had dropped to 49.7%. Suppose these results are based on a random sample of 1,800 people under 20 years old who were eligible to have a driver's license in year A and again in year B. At 95% confidence, what is the margin of error of the number of eligible people under 20 years old who had a driver's license in year A?

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cchilabert cchilabert · Answer 1 · 2020-02-08T22:16:12+01:00

Answer:

Step-by-step explanation:

Hello!

You have that the sample proportion of people under 20 years old that had a drivers licence is 0.619.

The statistic you use for a confidence interval for the population proportion is a Z and the formula for the confidence interval is

'p±[tex]Z_{1-\alpha /2}[/tex]*([tex]\sqrt{\frac{'p(1-'p)}{n} }[/tex] )

The margin of error of the interval is:

d= [tex]Z_{1-\alpha /2}[/tex]*([tex]\sqrt{\frac{'p(1-'p)}{n} }[/tex] )

d= [tex]Z_{0.975}[/tex]*([tex]\sqrt{\frac{'p(1-'p)}{n} }[/tex] )

d= [tex]1.965*\sqrt{\frac{0.619*0.381}{1800} }[/tex]

d= 0.022

I hope it helps!