AnswersCA-Statistics and Probability BEstimating the Difference between Two Population Proportions

Estimating the Difference between Two Population Proportions Answers

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Check the conditions for constructing a confidence interval for the difference in proportions.

Answers:
Random condition::met
10% condition::not met
Large Counts condition::not met
Are all the conditions for inference met?:No
2
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met✔ not metdoes not apply

A
met
B
not met
C
does not apply
3

met✔ not metdoes not apply

A
met
B
not met
C
does not apply
4

Yes✔ NoNot enough information

A
Yes
B
No
C
Not enough information
5

is notmay be✔ is

A
is not
B
may be
C
is
6

Check the conditions for constructing a confidence interval for the difference in proportions.

Answers:
Random condition::met
10% condition::does not apply
Large Counts condition::met
Are all the conditions for inference met?:Yes
7

Random condition: met 10% condition: met Large Counts condition: met All conditions for inference are met.Random condition: not met 10% condition: met Large Counts condition: met All conditions for inference are not metRandom condition: met 10% condition: does not apply Large Counts condition: met All conditions for inference are met.Random condition: met 10% condition: met Large Counts condition: not met All conditions for inference are not met.

A
Random condition: met 10% condition: met Large Counts condition: met All conditions for inference are met.
B
Random condition: not met 10% condition: met Large Counts condition: met All conditions for inference are not met
C
Random condition: met 10% condition: does not apply Large Counts condition: met All conditions for inference are met.
D
Random condition: met 10% condition: met Large Counts condition: not met All conditions for inference are not met.
8

Construct a 90% confidence interval to estimate the true difference in proportions pC – pD of caffeinated customers who order larges versus decaf customers who order larges.

Answers:
Are the conditions for inference met?:Yes
that the interval captures the true difference in proportions of caffeinated customers who larges versus decaf customers.:We are 90% confident
that the interval captures the true difference in proportions of caffeinated customers who larges versus decaf customers.:(0.048, 0.152)
that the interval captures the true difference in proportions of caffeinated customers who larges versus decaf customers.:would order
9

Researchers want to test a new hand exercise plan for arthritis patients to see if they have improved flexibility. They recruited 110 patients with arthritis in their hands and randomly assigned them to one of two treatment groups: group 1 took their regular medicine and did the new hand exercises; and group 2 only took medicine. After one month, 42 of the 55 in group 1 improved in their flexibility, and 37 of the 55 in group 2 improved their flexibility.Construct a 95% confidence interval to estimate the true difference in proportion pex – pnoex of patients like these who would show improvement in flexibility if they did the new hand exercises along with taking the medicine versus just taking the medicine.

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

Construct a 99% confidence interval to estimate the true difference in the proportion of “big” bank customers who bank with more than one bank as compared with the “small” customers who bank with more than one bank.

Answers:
A::0.4
B::2.576
C::200
D::300
11

A well-known coffee shop wants to estimate the difference in the proportion of caffeinated-coffee customers who order a large drink as compared with decaf-coffee customers who order a large. In a random sample of 500 caffeinated-coffee customers, 37% ordered larges. In a random sample of 370 decaf-coffee customers, 27% ordered larges.

Answers:
. Because contained in the interval, there is to believe there a difference in the proportions of caffeinated customers who order larges versus decaf customers who order larges.:Yes
. Because contained in the interval, there is to believe there a difference in the proportions of caffeinated customers who order larges versus decaf customers who order larges.:0
. Because contained in the interval, there is to believe there a difference in the proportions of caffeinated customers who order larges versus decaf customers who order larges.:is not
. Because contained in the interval, there is to believe there a difference in the proportions of caffeinated customers who order larges versus decaf customers who order larges.:convincing evidence
. Because contained in the interval, there is to believe there a difference in the proportions of caffeinated customers who order larges versus decaf customers who order larges.:is
12

Researchers want to test a new hand exercise plan for arthritis patients to see if they have improved flexibility. They recruited 110 patients with arthritis in their hands and randomly assigned them to one of two treatment groups: group 1 took their regular medicine and did the new hand exercises; and group 2 only took medicine. After one month, 42 of the 55 in group 1 improved in their flexibility, and 37 of the 55 in group 2 improved their flexibility.

Answers:
Because contained in the interval, there is to believe there a difference in the proportion of patients like these who would show improvement in flexibility if they did the new hand exercises along wi:0
Because contained in the interval, there is to believe there a difference in the proportion of patients like these who would show improvement in flexibility if they did the new hand exercises along wi:is
Because contained in the interval, there is to believe there a difference in the proportion of patients like these who would show improvement in flexibility if they did the new hand exercises along wi:not enough evidence
Because contained in the interval, there is to believe there a difference in the proportion of patients like these who would show improvement in flexibility if they did the new hand exercises along wi:is
13

A bank wants to estimate the difference in the proportion of its "big" customers who have a second account with a different bank and the proportion of its "small" customers who also have an account with another bank. Of the 200 “big” customers who were randomly selected, 160 claimed to also bank with other banks. Of the 300 “small” customers who were randomly selected, 120 claimed to also bank with other banks.

Answers:
Because contained in the interval, there is to believe there a difference in the proportion of “big” bank customers who bank with more than one bank as compared to the “small” customers who bank with:0
Because contained in the interval, there is to believe there a difference in the proportion of “big” bank customers who bank with more than one bank as compared to the “small” customers who bank with:is not
Because contained in the interval, there is to believe there a difference in the proportion of “big” bank customers who bank with more than one bank as compared to the “small” customers who bank with:convincing evidence
Because contained in the interval, there is to believe there a difference in the proportion of “big” bank customers who bank with more than one bank as compared to the “small” customers who bank with:is
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✔ does not applymetnot met

A
does not apply
B
met
C
not met
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We are 90% sure✔ We are 90% confidentWe are 90% certainThere’s a 90% probability

A
We are 90% sure
B
We are 90% confident
C
We are 90% certain
D
There’s a 90% probability
16

1.9602✔ 2.576

A
1.960
B
2
C
2.576
17

✔ 00.320.90

A
0
B
0.32
C
0.90
18

✔ isis not

A
is
B
is not
19

is✔ is not

A
is
B
is not
20

does not apply✔ metnot met

A
does not apply
B
met
C
not met

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