Question

Researchers in a populous country contacted more than​ 25,000 inhabitants aged 21 years to see if they had finished high​ school; 88.9 % of the 12 comma 873 males and 84.9​% of the 12 comma 971 females indicated that they had high school diplomas.

​a) What assumptions are necessary to satisfy the conditions necessary for​ inference?

​b) Create a 90​% 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? ​

a) What are the necessary​ assumptions?

A. Assume the samples do not include students from the same school.

B. Assume the samples are greater than​ 10% of the population.

C. Assume the samples are selected from a population that is approximately normal.

D. Assume the samples are independent and representative of all recent graduates.

​b) Create a 90​% confidence interval for the difference in graduation rates between males and​ females, p Subscript males Baseline minus p Subscript females. left parenthesis nothing comma nothing right parenthesis ​(Round to three decimal places as​ needed.)

​c) Choose the sentence below that best describes the confidence interval.

A. There is 90​% confidence that the graduation rate of males is greater than that of females by an amount in the interval.

B. There is 90​% confidence that the graduation rate in samples of 21​-year-old males will be greater than that of females by an amount in the interval.

C. There is 90​% confidence that the graduation rate of 21​-year-old males is greater than that of 21​-year-old females by an amount in the interval.

​d) Is there evidence of a difference in the graduation​ rates?

A. There is no evidence that the graduation rate of boys is different than girls.

B. There is evidence that the graduation rate of boys is greater than girls.

C. There is evidence that the graduation rates of boys and girls are the same.

D. There is evidence that the graduation rate of boys is less than girls.

Answer 1

b)

90% confidence interval

(0.0331,0.0469)

c)

option C) is correct

C. There is 90​% confidence that the graduation rate of 21​-year-old males is greater than that of 21​-year-old females by an amount in the interval.

d)

since lower bound is greater than 0,

option B) is correct

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