Question

In: Statistics and Probability

A researcher wanted to test the claim that, "Seat belts are effective in reducing fatalities." A...

A researcher wanted to test the claim that, "Seat belts are effective in reducing fatalities." A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were killed. If a significance level of 5% is used, which of the following statements gives the correct conclusion?

Question 7 options:

A)	Since , we conclude that this data shows that seat belts are effective in reducing fatalities.

B)	Since , we conclude that this data shows that seat belts are effective in reducing fatalities.

C)	Since , we conclude that this data shows that seat belts aren't effective in reducing fatalities.

D)	Since , we conclude that this data shows that seat belts aren't effective in reducing fatalities.

Expert Solution

Let be the proportion of occupants not wearing the seat belts who got killed and be the proportion of occupants wearing the seat belts who got killed. Therefore, we have:

Null and Alternative hypothesis:

Under Ho: the null hypothesis :

our test statistic is:

p-value = P(z>6.11)=0.00000. Since p-value is less than , we have sufficient evidence to rejectHo at 5% level of significance.

A)	Since , we conclude that this data shows that seat belts are effective in reducing fatalities.

B)	Since , we conclude that this data shows that seat belts are effective in reducing fatalities.

Both the statements are the same so i think you can mark either of them. but at 5% level of significance.

orchestra answered 2 years ago

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