Probilibty Question a Study

[srt927]

In a study of air-bag effectiveness, it was found that in 821 crashes of midsize cars equipped with air bags, 46 of the crashges resulted in hospitalization. Use a .01 significance level to test the claim that air-bag hospitalization rate is lower than the 7.8% rate for crashes of mid-size cars equipped with automatic safety belts.

I'm lost I know the Test statistic formula but not sure how I determine where to plug them into the formula.

 

[galactus]

\(\displaystyle \L\\\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}}\)

This is proportions instead of means, but the principle is the same.

Find your proportion p, 46/821

Set up your hypotheses:

\(\displaystyle \L\\H_{0}\geq{7.8%}\)

\(\displaystyle \L\\H_{a}<7.8% \;\ (claim)\)

You have a left-tailed test with a 1% level of significanc. Test away.