Question

A random sample of college students who owned cars revealed the following: out of 105 cars, 28 had stick shifts. Estimate the proportion of college students who drive stick shift cars with 90% confidence. Give the upper limit of the confidence interval, rounded to three places after the decimal point.

Answer 1

The sample proportion is as follows

`p=(28)/(105)=0.26666666666=0.267`

The confidence interval formula can be represented below

`p\pm z*\sqrt[]{(p(1-p))/(n)}`[tex]\begin{gathered} 0.267\pm1.645\times\sqrt[]{\frac{0.267(1-0.267)}{105}} \\ 0.267\pm1.645\times\sqrt[]{\frac{0.195711}{105}} \\ 0.267\pm1.645\times\sqrt[]{0.00186391428} \\ 0.267\pm0.0710197061 \\ 0.267-0.0710197061

upper limit = 0.338