Instead of paying to support welfare recipients, many people want them to find j
ID: 3131708 • Letter: I
Question
Instead of paying to support welfare recipients, many people want them to find jobs. If necessary, they want each province to create public service jobs for those who cannot find jobs in private industry. In a survey of 800 voters, 400 Conservatives (population 1) and 400 Liberals (population 2), 75% of the Conservatives and 90% of the Liberals favored the creation of public service jobs. Use a 95% large-sample confidence interval estimation procedure to compare the difference between the proportions of Conservatives and Liberals who favor creating public service jobs in the population of registered voters[5]. Explain your conclusions [2].
Explanation / Answer
a)
Let
p1 = population proportion of conservatives who favored the creation of public service jobs
p2 = population proportion of liberals who favored the creation of public service jobs
Getting p1^ and p2^,
p1^ = x1/n1 = 0.75
p2 = x2/n2 = 0.9
Also, the standard error of the difference is
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] = 0.026339134
For the 95% confidence level, then
alpha/2 = (1 - confidence level)/2 = 0.025
z(alpha/2) = 1.959963985
Margin of error = z(alpha/2)*sd = 0.051623755
lower bound = p1^ - p2^ - z(alpha/2) * sd = -0.201623755
upper bound = p1^ - p2^ + z(alpha/2) * sd = -0.098376245
Thus, the confidence interval is
( -0.201623755 , -0.098376245 ) [ANSWER]
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b)
As we can see, the whole interval is negative. Hence, there is significant evidence at 95% confidence that the population proportion of conservatives who favored the creation of public service jobs is less than the population proportion of liberals who favored the creation of public service jobs. [CONCLUSION]