Nationwide data from 1998 shows that there were approximately 2,150 motorcyclist

Question

Nationwide data from 1998 shows that there were approximately 2,150 motorcyclist fatalities for about 3,725,000 motorcycle registrations in the US.

That same year, as mentioned above, the state of Texas experienced 132 motorcyclist fatalities, with 149,175 registered motorcycles.

Taking the US data to constitute a population proportion p, perform a significance test to determine whether or not the motorcyclist fatality rate in Texas was significantly different than the US population motorcyclist fatality rate, with a significance level of 0.01.

Do the problem as number of fatalities per thousand registered motorcycles, i.e. your sample size is n=149.175 for Texas and the proportion of fatalities is 2150 / 3725. Then calculate the 99% CI, and state your conclusion and what it tells you.

Explanation / Answer

Ho : P1 = p2

Ha :P1 is not p2

P1 =2150 /  3725000 = 0.000577

P2 = 132 / 149 175 = 0.00082

P = ( 2150 + 132 ) / ( 3725000 + 147175) = 0.00059

Z = ( 0.00082 - 0.000577) / ( srqt 0.00059 * 0.99941 * ( 1 / 3725000+1/147175) )

Z = 3.765

for alpha = 0.01 alpha / 2 = 0.005 critical value is 2.57

since Z > critical value

we conclude that  fatality rate in Texas was significantly different than the US population motorcyclist fatality rate, with a significance level of 0.01.

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