Is there any difference between the proportion of americans who wish they were r

Question

Is there any difference between the proportion of americans who wish they were rich and the proportion of canadians who wish they were rich? A random sample of 1,000 americans showed that 550 wish they were rich, while a ranndom sample of 500 canadians showed that 225 wish they were rich.

a. Find a 97.5% confidence interval for the difference between the population proportions who wish they were rich.

b. Test at the 1% level of significance, whether the two population proportions are significantly different. Formulate and test the appropriate hypotheses. Use the critical value approach.

Explanation / Answer

p1^=550/1000=0.55

p2^=225/500=0.45

H0:P1=p2

Ha:p1 != p2

test statistics=(0.55-0.45)/sqrt(0.55*0.45/1000+0.45*0.55/500)=3.67

critical values=+/- 2.58

at test statistics falls outside interval (-2.58 , 2.58) we can reject H0

so there is significant difference between the proportion of americans who wish they were rich and the proportion of canadians who wish they were rich

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