A random sample of 500 adult residents of Maricopa County found that 385 were in

Question

A random sample of 500 adult residents of Maricopa County found that 385 were in favor of increasing the highway speed limit to 75 mph. while another sample of 400 residents of Pima County found that 267 were in favor of the increased speed limit.

a. Do these data indicate that there is a difference in the support for increasing the speed limit to 75 mph between the residents of the two counties? Use = 0.05. What is the p-value of this test?

b. Construct a 95% confidence interval on the difference in the two proportions. Provide a practical interpretation of this interval.

Explanation / Answer

Given n1=500n2=400x1=385x2= 267

p1=x1/n1 = 0.77p2=x2/n2 =0.6675

q1=1-p1 = 0.23q2=1-p2=0.3325

P =(x1+x2)/(p1+p2) =0.7244

Q=1-P = 0.2756

The null hypothesis is

H0: P1-P2=75mph.i.e., there is no diffrernce in the speed limit.

Against the alternative hypothesis

H1:P1-P2>75.i.e., there is a difference in the speed limit

The test statistic is

Z= p1-p2/sqrt(P*Q*((1/n1)+(1/n2))

Z= 0.77-0.6675/sqrt(0.7244*0.2756*(0.002+0.0025)

Here the table value is given by 1.96 at 0.05 level of significance

Therefore Zcal> Ztab we reject the null hypothesis hence there is a diference in the speed limit

The p value is 0.00062. the result is significant at p<0.05

S.E(p1-p2)= sqrt((p1q1/n1)+(p2q2/n2)) = 0.03

95%confidence interval is (p1-p2)1.96*S.E(p1-p2)

[0.04370 ,0.16130]

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