Question

Researchers in a populous country contacted more than​ 25,000 inhabitants aged

23

years to see if they had finished high​ school;

89.9 %

of the

12,687

males and

86.3​%

of the

12 849

females indicated that they had high school diplomas.

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

​b) Create a

99​%

confidence interval for the difference in graduation rates between males and​ females,

p Subscript males Baseline minus p Subscript femalespmales−pfemales.

​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 are independent and representative of all recent graduates.

This is the correct answer.

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 do not include students from the same school.

Your answer is not correct.​b) Create a

95​%

confidence interval for the difference in graduation rates between males and​ females,

p Subscript males Baseline minus p Subscript femalespmales−pfemales.

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

95​%

confidence that the graduation rate of

malemales

is greater than that of

femalesfemales

by an amount in the interval.Your answer is not correct.

B.There is

95​%

confidence that the graduation rate of

25​-year-old

male

is greater than that of

25​-year-old

female

by an amount in the interval.This is the correct answer.

C.There is

95​%

confidence that the graduation rate in samples of

25​-year-old sales

will be greater than that of

female

by an amount in the interval.

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

A.There

isis

evidence that the graduation rate of

boys

is

greater

than

girls

B.There is evidence that the graduation rates of

boys

and

girls

are the same.

C.There

is nois no

evidence that the graduation rate of

boys

is

different

than

girls

D.There

is

evidence that the graduation rate of

boys

is

less

than

girls

Answer 1

a)

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

b)

(c)

We are 99% confidence interval, that true difference in proportion lies in the above interval.

d)

No because confidence interval have all positive values.