Question

In the survey on the death penalty you read about in the chapter, the Gallup Poll actually split the sample at random, asking 510 respondents the question quoted earlier, “Generally speaking, do you believe the death penalty is applied fairly or unfairly in this country today?” The other 510 were asked “Generally speaking, do you believe the death penalty is applied unfairly or fairly in this country today?” Seems like the same question, but sometimes the order of the choices matters. Asked the first question, 58% said the death penalty was fairly applied; only 54% said so with the second wording. a) What kind of bias may be present here? b) If we combine them, considering the overall group to be one larger random sample of 1020 respondents, what is a 95% confidence interval for the proportion of the general public that thinks the death penalty is being fairly applied? c) How does the margin of error based on this pooled sample compare with the margins of error from the separate groups? Why?

          In the survey on the death penalty you read about in the chapter, the Gallup Poll actually split the sample at random, asking 510 respondents the question quoted earlier, “Generally speaking, do you believe the death penalty is applied fairly or unfairly in this country today?” The other 510 were asked “Generally speaking, do you believe the death penalty is applied unfairly or fairly in this country today?” Seems like the same question, but sometimes the order of the choices matters.
Asked the first question, 58% said the death penalty was fairly applied; only 54% said so with the second wording.
a) What kind of bias may be present here?
b) If we combine them, considering the overall group to be one larger random sample of 1020 respondents, what is a 95% confidence interval for the proportion of the general public that thinks the death penalty is being fairly applied?
c) How does the margin of error based on this pooled sample compare with the margins of error from the separate groups? Why?

Show more…

Added by Gregorio H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Joanna Quigley

11/11/2022

Step 1

This occurs when the order in which the options are presented influences the responses. In this case, the option presented first ("fairly" in the first question and "unfairly" in the second question) received a higher percentage of responses. b) To calculate the Show more…

Show all steps

lock

Thanks for your feedback!

In the survey on the death penalty you read about in the chapter, the Gallup Poll actually split the sample at random, asking 510 respondents the question quoted earlier, “Generally speaking, do you believe the death penalty is applied fairly or unfairly in this country today?” The other 510 were asked “Generally speaking, do you believe the death penalty is applied unfairly or fairly in this country today?” Seems like the same question, but sometimes the order of the choices matters. Asked the first question, 58% said the death penalty was fairly applied; only 54% said so with the second wording. a) What kind of bias may be present here? b) If we combine them, considering the overall group to be one larger random sample of 1020 respondents, what is a 95% confidence interval for the proportion of the general public that thinks the death penalty is being fairly applied? c) How does the margin of error based on this pooled sample compare with the margins of error from the separate groups? Why?

Play audio

Feedback

Powered by NumerAI

Joanna Quigley and 63 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 We're looking at a survey on the death penalty.

00:03 Half of the people were asked, do you believe it is applied fairly or unfairly? the other half were asked, is it unfairly or fairly? what kind of bias we're seeing here is we get different results? this is a form of response bias, and specifically it is order bias.

00:23 People respond differently depending on what order the questions or the outcomes come in.

00:30 In this case, the possible options they could choose came in different orders, and that affected the responses.

00:39 Part b, we're now going to combine them into an overall group.

00:43 So now our overall group has a sample size of 1 ,020, and the sample proportion, who said it was fairly applied, so 58 % for half of them, 54 % for half of them, the average is going to be between them.

01:02 We don't need to take a weighted average in this case.

01:06 If the sample sizes for each group were different, you would have to do a weighted average.

01:11 But since they're the same here, i'm just going halfway between.

01:14 So this is the proportion of this overall group who thought it was fairly applied.

01:19 We need to take a 95 % confidence interval.

01:22 So the formula for a confidence interval, for a proportion, when you have a nice big sample size, is p -hat, your point estimate, plus and minus your margin of error, which is z root p hat 1 minus p hat over n.

01:40 This is the formula we're going to use.

01:42 We have n, we have p hat, we get z from the level of confidence.

01:47 So z is from the normal distribution.

01:51 And when you have a proportion with a nice big sample size like this, you have an approximately normal approximation to it.

02:01 So here's my normal approximation.

02:03 I have my p hat in the middle.

02:04 And i'm saying, i'm going to put down a confidence interval where 95 % of sample proportions and the original population proportion is in here somewhere, 95 % of values of this curve are in my interval.

02:18 5 % are in the tails.

02:20 This is symmetric.

02:22 So each tail is 2 .5%...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later