In an ongoing nationwide survey, a question asked is whether a respondent favors or opposes capital punishment (the death penalty) for persons convicted of murder. The output for this exercise...

In an ongoing nationwide survey, a question asked is whether a respondent favors or opposes capital punishment (the death penalty) for persons convicted of murder. The output for this exercise compares the proportions who said that they were opposed to the death penalty in the year 2008 and the year 1993.

Sample	X	N	Sample p
2008	637	1912	0.333
1993	333	1418	0.235

Estimate for

p(1) − p(2): 0.098

95% CI for

p(1) − p(2): (0.068, 0.129)

(a)

What proportion of the year 2008 sample was opposed to the death penalty? (Round your answer to three decimal places.)

What proportion of the year 1993 sample was opposed? (Round your answer to three decimal places.)

(b)

What is the estimated difference between the proportions opposed to the death penalty in the 2 years? (Use

p₂₀₀₈
− p₁₉₉₃.

Round your answer to three decimal places.)

(c)

Write the 95% confidence interval as it is given in the output.

Interpret this interval in the context of this situation.

There is a 95% chance that, for the two years, the population difference in proportions who said that they were opposed to the death penalty is within the interval.We are 95% confident that, for the two years, the population difference in proportions who said that they were opposed to the death penalty is the midpoint of the interval. There is a 95% chance that, for the two years, the population difference in proportions who said that they were opposed to the death penalty is outside the interval.We are 95% confident that, for the two years, the population difference in proportions who said that they were opposed to the death penalty is outside the interval.We are 95% confident that, for the two years, the population difference in proportions who said that they were opposed to the death penalty is within the interval.

(d)

Provide the formula used to calculate the interval.

(p̂₁
− p̂₂) ± z*

(p̂₁
− p̂₂)(1 − (p̂₁
− p̂₂))

n₁
+ n₂

(p̂₁
− p̂₂) ± z*

p̂₁(1 − p̂₁)

n₁

p̂₂(1 − p̂₂)

n₂

(p̂₁
− p̂₂) ± z*

p̂₂(1 − p̂₂)

n₁

p̂₁(1 − p̂₁)

n₂

(p̂₁
− p̂₂) ± z*

p̂₁p̂₂

n₁
+ n₂

(p̂₁
− p̂₂) ± z*

p̂₁(1 − p̂₁) + p̂₂(1 − p̂₂)

n₁
+ n₂

Substitute appropriate numerical values into the formula.

(0.333 − 0.235) ± 1.96

(0.333 − 0.235)(1 − (0.333 − 0.235))

1,912 + 1,418

(0.333 − 0.235) ± 1.96

0.235(1 − 0.235)

1,912

0.333(1 − 0.333)

1,418

(0.333 − 0.235) ± 1.96

0.333(1 − 0.333)

1,912

0.235(1 − 0.235)

1,418

(0.333 − 0.235) ± 1.96

0.333(1 − 0.333) + 0.235(1 − 0.235)

1,912 + 1,418

(0.333 − 0.235) ± 1.96

0.333(0.235)

1,912 + 1,418

Jun 09, 2022

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In an ongoing nationwide survey, a question asked is whether a respondent favors or opposes capital punishment (the death penalty) for persons convicted of murder. The output for this exercise...

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