Drive While Drowsy? Yes Yes No Yes No Yes No Yes No Yes No Yes No No Compute 500

Question

Drive While Drowsy? Yes Yes No Yes No Yes No Yes No Yes No Yes No No Compute 500 times Yes Yes No Yes No In a cover story, BusinessWeek noted that sleep deprivation was a leading cause of traffic accidents and fatalities. 51% of adults admitted to driving while drowsy. A leading sleep expert hypothesized that this problem was even bigger for those who work the night shift. He designed a study to test his hypothesis. No Yes No No Yes Develop the correct hypothesis. No No No No Yes Develop a point estimate of the number of people in the study who admit to driving while drowsy. No Yes What is the sample proportion? Yes Yes What is the p-value? No Yes At the 0.99 level of significance, can we reject the null hypothesis? No No What conclusion can we draw based upon this sample? Yes No Yes If we make an error here, is it a Type I or Type II error? Drive While Drowsy? Yes Yes No Yes No Yes No Yes No Yes No Yes No No Compute 500 times Yes Yes No Yes No In a cover story, BusinessWeek noted that sleep deprivation was a leading cause of traffic accidents and fatalities. 51% of adults admitted to driving while drowsy. A leading sleep expert hypothesized that this problem was even bigger for those who work the night shift. He designed a study to test his hypothesis. No Yes No No Yes Develop the correct hypothesis. No No No No Yes Develop a point estimate of the number of people in the study who admit to driving while drowsy. No Yes What is the sample proportion? Yes Yes What is the p-value? No Yes At the 0.99 level of significance, can we reject the null hypothesis? No No What conclusion can we draw based upon this sample? Yes No Yes If we make an error here, is it a Type I or Type II error?

Explanation / Answer

let p=propotion of adults admitted to driving while drowsy

null hypothesis H0:P=0.51

alternate hypothesis H1:P>0.51

number of yes=19

number of no=21

n=40

proportion of yes=p=19/40=0.475

here we use z-test and z=(p-P)/SE(p)=(0.475-0.51)/sqrt(0.51*(1-0.51/40))=-0.0493

0.99 confidence level one tailed critical z(0.01)=2.32 is more than calcualted z=-0.0493, so we fail to reject H0 and conclude that propotion of adults admitted to driving while drowsy is 51%.

here we are accepting null hypothesis so we may commit type II error

Type II error ::accepthing H0 when it is false

Type I error: rejection H0 when it is true

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