Question

Researchers in a populous country contacted more than​ 25,000 inhabitants aged 23 years to see if they had finished high​ school; 85.9 % of the 12 comma 983 males and 80.2​% of the 12 comma 921 females indicated that they had high school diplomas. ​a) What assumptions are necessary to satisfy the conditions necessary for​ inference? ​b) Create a 95​% confidence interval for the difference in graduation rates between males and​ females, p Subscript males Baseline minus p Subscript females. ​c) Interpret your confidence interval. ​d) Is there evidence that boys are more likely than girls to complete high​ school?

Answer 1

(a) Assume the samples are independent and representative of all recent graduates.

(b) (0.048, 0.066)

(c) There is a 95% confidence that the graduation rate of 25-year-old males is greater than that of 25-year-old females by an amount in the interval.

(d) There is evidence that the graduation rate of boys is greater than girls.

p1	p2	pc
0.859	0.802	0.8306	p (as decimal)
11152/12983	10363/12921	21515/25904	p (as fraction)
11152.397	10362.642	21515.039	X
12983	12921	25904	n
	0.057	difference
	0.	hypothesized difference
	0.0047	std. error
	12.23	z
	0.00E+00	p-value (two-tailed)
	0.048	confidence interval 95.% lower
	0.066	confidence interval 95.% upper
	0.0091	margin of error

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