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iVinArrow [24]
3 years ago
8

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​%)
Mathematics
1 answer:
ss7ja [257]3 years ago
7 0

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

Step-by-step explanation:

Given : Sample space : n= 559

Sample proportion : \hat{p}=\dfrac{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{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.1628\pm (1.96)\sqrt{\dfrac{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\%)

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