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: p8くPN. (Use standard error-0.116.) (3 decimal places) (b) Determine the p-value (3 decimal places) (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? 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 lower than the proportion of New York drivers wearing seat belts. The proportion of Boston drivers wearing seat belts was significantly higher than the proportion of New York drivers wearing seat belts

Answer 1

(A.)test statistic for this test using Ha: p8くPN is Z = -2.164 (B.) p-value (3 decimal places) is 0.015. (C.) Based on this p-value, which of the following would you expect for a 95% is negative. (D.) the correct conclusion is The proportion of Boston drivers wearing seat was significantly lower than the proportion of new York drivers wearing seat belts.

A.)

According to given data find the test statistic for this test using Ha:

p1 = 0.581

p2 = 0.832

standard error = SE = 0.116

Test statistics :-

Z = $\frac{p1 - p2}{SE}$

Z = $\frac{0.581 - 0.832}{0.116}$ = -2.164

Z = -2.164

B.)

According to given Determine the p-value (3 decimal places).

p - value

it is left tailed test.

p - value for left tailed test is,

p - value = P(Z < test statistics )

p - value = P(Z < -2.164)

P - value = 0.015

C.)

Based on this p-value, which of the following would you expect for a 95%

confidence level = 95% = 0.95

significance level = α = 0.05

P -value is less than 0.05

so, reject null hypothesis at α = 0.05

That is $P_{B}$ < $P_{NY}$

so, based on P - value , All values in the 95% confidence interval

PB - PNY  is negative.

D.)

According to given data What is the correct conclusion?

Reject null hypothesis at α = 0.05

so, $P_{B}$ < $P_{NY}$

Hence, The proportion of Boston drivers wearing seat was significantly lower than the proportion of new York drivers wearing seat belts.

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