Question

The article "College Graduates Break Even by Age 33" reported that 5.7% of high school graduates were unemployed in 2008 and 9.7% of high school graduates were unemployed in 2009.† Suppose that the reported percentages were based on independently selected representative samples of 300 high school graduates in each of these two years.

(a)Construct a 99% confidence interval for the difference in the proportion of high school graduates who were unemployed in these two years. (Use p2008 − p2009. Round your answers to three decimal places.)

B) The same article reported that 2.6% of college graduates were unemployed in 2008 and 4.6% of college graduates were unemployed in 2009. Suppose that the reported percentages were based on independently selected representative samples of 500 college graduates in each of these two years. A 95% confidence interval for the difference in the proportion of college graduates who were unemployed in these two years was calculated to be (−0.043, 0.003). Is the confidence interval from part (a) wider or narrower than this confidence interval? (Round your answers to three decimal places.)The width of the confidence interval in part (a) is _______ and the width of the given confidence interval is _________ . Thus, the confidence interval in part (a) is

Answer 1

The article "College Graduates Break Even by Age 33" reported that 5.7% of high school graduates were unemployed in 2008 and 9.7% of high school graduates were unemployed in 2009.† Suppose that the reported percentages were based on independently selected representative samples of 300 high school graduates in each of these two years.

(a)Construct a 99% confidence interval for the difference in the proportion of high school graduates who were unemployed in these two years. (Use p2008 − p2009. Round your answers to three decimal places.)

99% CI = (-0.096, 0.016)

CI = p1-p2 ± z*se

99% z value =2.576

Standard error of p1-p2= se=

Hypothesis test for two independent proportions
	p1	p2	pc
	0.057	0.097	0.077	p (as decimal)
	17/300	29/300	46/600	p (as fraction)
	17.1	29.1	46.2	X
	300	300	600	n
	difference	-0.04
	confidence interval 99.% lower	-0.0959
	confidence interval 99.% upper	0.0159
	margin of error	0.0559

B) The same article reported that 2.6% of college graduates were unemployed in 2008 and 4.6% of college graduates were unemployed in 2009. Suppose that the reported percentages were based on independently selected representative samples of 500 college graduates in each of these two years. A 95% confidence interval for the difference in the proportion of college graduates who were unemployed in these two years was calculated to be (−0.043, 0.003). Is the confidence interval from part (a) wider or narrower than this confidence interval? (Round your answers to three decimal places.)

The width of the confidence interval in part (a) is 0.112 and the width of the given confidence interval is 0.046 .

Thus, the confidence interval in part (a) is wider.