A study was conducted to compare the proportion of drivers in Boston and New Yor

Question

A study was conducted to compare the proportion of drivers in Boston and New York who wore seat belts while driving. Data were collected, and the proportion wearing seat belts in Boston was 0.581 and the proportion wearing seat belts in New York was 0.832.

Due to local laws at the time the study was conducted, it was suspected that a smaller proportion of drivers wear seat belts in Boston than New York.

(a) Find the test statistic for this test using Ha: pB < pNY. (Use standard error = 0.095.)

(b) Determine the p-value.

(c) Based on this p-value, which of the following would you expect for a 95% confidence interval for pB - pNY?
All values in the interval are negative.

Some values in the interval are positive and some are negative.     

All values in the interval are positive.
(d) What is the correct conclusion?
The proportion of Boston drivers wearing seat belts was significantly lower than the proportion of New York drivers wearing seat belts.

There was no significant difference between the proportion of drivers wearing seat belts in Boston and New York.    

The proportion of Boston drivers wearing seat belts was significantly higher than the proportion of New York drivers wearing seat belts.

Explanation / Answer

a) Test statistic

= (0.581 - 0.832)/0.095

= -2.64

b) p - Value = P(z < -2.64) = 0.0041

c) All values in the interval are negative.

d) Correct conclusion: The proportion of Boston drivers wearing seat belts was significantly lower than the proportion of New York drivers wearing seat belts. Option A is correct.

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