Question

To determine if there is a significant difference in the proportion of smokers among the
blue collar workers of the United States and Italy, two independent random samples of sizes
1000 and 850 are taken from both populations respectively. If 420 in the U.S. sample are
smokers and 350 in the Italy sample are smokers .Test the claim that the proportion of blue collar smokers is higher in the U.S. than Italy.
Use α = 0.05.

Fill in the blanks

State the null and alternative hypothesis

Ho: p1 p2

H1: p1 p2

The test statistics is . Round your answer in 2 decimal places

The critical value is . Round your answer in 2 decimal places

The P-value is . Round your answer in 2 decimal places.

Decision

A) Reject the Ho

B) Do not reject the Ho

Type A or B in the box

Conclusion:

A) We can conclude that the proportion of blue collar smokers is higher in the U.S. than Italy.

B) We can not conclude that the proportion of blue collar smokers is higher in the U.S than Italy.

Type A or B in the box

Answer 1

Ho: p1=p2

H1: p1 > p2

	US	Italy
x=	420	350
p̂=x/n=	0.4200	0.4118
n =	1000	850
estimated prop. diff =p̂1-p̂2    =		0.0082
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.4162
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0230
test stat z=(p̂1-p̂2)/Se =		0.36

for 0.05 level with right tailed test , critical value of z=

1.64

P value   =

0.36

(from excel:1*normsdist(-0.36)

Decision :

B) Do not reject the Ho (since p value >0.05)

Conclusion":

B) We can not conclude that the proportion of blue collar smokers is higher in the U.S than Italy.