Question

insurance company checks police records on 559 accidents selected at random and notes that teenagers were at the wheel in 91 of them. Use this information to complete parts a through d below.​a) Create a​ 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.​(nothing​%,nothing​%)

Answer 1

Answer:
`(13.22\%,\ 19.34\%)`

Explanation:

Given : Sample space : n= 559

Sample proportion :
`\hat{p}=(91)/(559)=0.162790697674\approx0.1628`

`=16.28\%`

Significance level :
`\alpha= 1-0.95=0.05`

Critical value :
`z_(\alpha/2)=1.96`

Confidence level for population proportion:-

`\hat{p}\pm z_(\alpha/2)\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\=0.1628\pm (1.96)\sqrt{(0.1628(1-0.1628))/(559)}\\\\=0.1628\pm0.030604971367\\\\\approx 0.1628\pm0.0306=(0.1322,\ 0.1934)=(13.22\%,\ 19.34\%)`

Hence, 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.=
`(13.22\%,\ 19.34\%)`