Confidence Interval, Hypothesis
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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 1000 Americans showed that 550 wish they were rich, while a random sample of 500 Canadians showed that 225 wished they were rich.
a. Find a 97.5% confidence interval for the difference between the population proportions who wish they were rich.
Note: Express your answer to 4 decimal places of accuracy.
b. Test, at the 1% level of significance, whether the two population proportions are significantly different. Formulate and test the appropriate hypothesis. Use the critical value approach.
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(a)
n1 = 1000, n2 = 500, p1 = 550/1000 = 0.55, p2 = 225/500 = 0.45
p1 - p2 = 0.55 - 0.45 = 0.10
p = (n1p1 + n2p2)/(n1 + n2) = (550 + 225)/(1000 + 500) = 0.51667
q = 1 - p = 0.48333
Standard Error of the difference between population proportions = √[pq{(1/n1) + (1/n2)}]
SE = √[0.51667 * 0.48333 * {(1/1000) + (1/500)}] = ...
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