Question

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A random sample of 200 cars has 18 that are green in color. What is the...

A random sample of 200 cars has 18 that are green in color. What is the confidence interval for the true proportion of green cars that lie within a 95% confidence interval?

Expert Solution

Solution :

Given that,

n = 200

x = 18

Point estimate = sample proportion = = x / n = 0.09

1 - = 0.91

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z_{/ 2} * $\sqrt$ (( * (1 - )) / n)

= 1.96 * ( $\sqrt$ ((0.09 * 0.91) / 200)

= 0.040

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.09 - 0.040 < p < 0.09 + 0.040

0.050 < p < 0.130

The 95% confidence interval is ( 0.050 , 0.130 )

milcah answered 1 year ago

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