Question

Candy has observed 250 sports cars at an intersection and found that 15% did not make a complete stop. Candy tells you that the margin of error was 8%. What was the confidence level of the study?

Answer 1

The confidence level of the study is 99.9%

The confidence level is 99.9% of the margin error is 8%

Explanation:

Explanation:-

Candy has observed 250 sports cars

The sample size 'n' = 250

Sample proportion 'p' = 15% = 0.15

The margin of error = 8% = 0.08

The margin of error is determined by =
`(z_(\alpha )√(p(1-p)) )/(√(n) )`

`0.08 X √(250) = z_(\alpha ) √(0.15 (1-0.15))`

`( 0.08 X √(250))/( √(0.15 (1-0.15))) = z_(\alpha )`

`z_(\alpha )= ( 0.08 X √(250))/( √(0.15 (1-0.15))) = (1.2649)/(0.35707)`

`z_(\alpha ) = 3.5431`

Conclusion:-

The z- score of 99.9% level of significance = 3.54 for two tailed test

Hence the confidence level is 99.9% of the margin error is 8%.