Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

A Pew Research Center survey asked respondents if they would rather live in a place with a slower pace of life or a place with a faster pace of life $(U S A$ Today, February $13,2009) .$ Consider the following data, which show a sample of preferences expressed by 150 men and 150 women.a. Combine the samples of men and women. What is the overall percentage of respondents who prefer to live in a place with a slower pace of life? What is the overall percentage of respondents who prefer to live in a place with a faster pace of life? What is your conclusion?b. Is the preferred pace of life independent of the respondent? Use $\alpha=.05 .$ What is yourconclusion? What is your recommendation?

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

a. $71 \%, 22 \%$b. There is not sufficient evidence to support the claim that the variablesare not independent.

Intro Stats / AP Statistics

Chapter 11

Comparisons Involving Proportions and a Test of Independence

Descriptive Statistics

Confidence Intervals

The Chi-Square Distribution

Piedmont College

Cairn University

Oregon State University

Lectures

0:00

03:28

A Pew Research Center surv…

06:54

A Pew Research Center …

02:38

The Pew Research Center&#x…

02:51

Planning-habits survey. Am…

03:27

Where do young adults live…

07:47

According to the Current P…

03:06

A survey by the National I…

02:37

In $2000,25.8 \%$ of Ameri…

and this question, the first thing we're asked to find is the overall percentage of respondents who prefer to live in a place with a slower pace of life. So for this report, A all that we're going to do is find the percent of respondents that one a slower pace of life. So we have to do is add 102 and 1 11 and divide it by our grand total. By the way, I create. I came up with these totals, um, for the column totals thes totals down here. I summed up the values in each column and then for the road totals. I did the same thing. These totals over here. I did the same thing, except I summed the rose. So one and two and then the grand total over here in blue is just the, um, column total summed, or it's also the road total sum. So what we need to do is figure out the total number of people who want a slower pace of life. We figured that to be to 13 so this is the proportion with the slower pace of life over the proportion of or over the grand total, which is 300. So this is equal to 2 13 over 300 with times 0.71 4.100 or sorry, times 100 to get a percentage. So we get 71%. And now we have to do the same thing, but with a faster pace of life. So we will add 39 27 to get the total number of people who prefer a faster pace of life, which is 66 66 divided by 300 is equal to 3000.22 point 22 times 100 is equal to 22%. So these air answers too far A and part B. Now we have to check whether the pace of life and gender or independent of each other or not. So we will go to our No, an alternative hypothesis to come up with these. So are no hypothesis would be that boom pace of life and gender are independent of each other on DDE. Our alternative hypothesis would be that they are not independent. So I'm gonna use abbreviations. So, um, for the pace of life, I'm just gonna write p o l and gender g are not independent. So now how do we test our hypothesis? Ah, we have to come up with the chi squared value. So the chi squared value is simply the or not simply, but it is the, um observed frequency for each row and column combination minus the expected frequency for each Rohan column combination squared, divided by the expected frequency for each Roman column combination. So the first thing we have to do is figure out howto find are expected, um frequency and the expected frequency is just the ah ro total. So the row total times the column total divided by the grand total. So for men and slower men who prefer a slower pace of life, the expected proportion the expected frequency would be, uh, one under two. Sorry, not 100 to 213 because that is our road total 213 our row total times our column total of 1 50 divided by our grand total of 300. So are expected frequency for men who prefer a slower pace of life would be 106.5. So we do this for each value in our table for each cell and we come up with the following, Um, with the following table, Uh, this will expand. So these this is our expected frequency table. And now we can use this to come up with our chi squared, but not yet. This is a middle step. So what we need to do now is where Kai squared. We were told that we need to take the difference between the observed frequency and the expected frequency, square it and divide it by the expected frequency. So let's do the math for that. So, in our chi square, if we're still using, um, the men who prefer a slower pace of life Ah, cell that would be 102 102 minus 106.5 squared, divided by one of six going to five. And now, using this value, we can using this set up, we can get all the values in this cell following this formula, this will expand. Um, Okay. So, uh, this is the difference. Squared. This right here is the difference squared. Divided by the expected for men. Who prayers, slower pace of life. This is the difference Squared, divided by the expected for men who prefer who have no preference. And this is the difference squared, divided by the expected from men who prefer a faster pace of life. This is the difference squared, divided by the expected for women who prefer a slower pace of life. This is a different squared, Um, for when you prefer who have no preference. And this is a different squared for women who prefer a faster pace of life. Now our chi squared is going to be the sum of each individual value here of all ourselves. So once we take our, um, some, we get a chi square of 2.98 of approximately 2.98 That's art 2.99 approximately 2.99 But ah, this is not enough to find our p value to find our P value. We also need to come up with the degrees of freedom. Are degrees of freedom is the number of rows We have minus one times the number of columns. We have minus one, and we have to rose so two minus one times, uh, three columns. So this is equal to one times two. So our degrees of freedom is equal to two. So our P value given that ark I squared is 2.99 and we have two degrees of freedom is equal to approximately is greater than 0.1 Torpey value is greater than 0.1. And now we have to compare our p value greater than 0.12 are Alfa of 0.5 So because our Alfa equals 0.5 is less than 0.1, which is less than r p value, we have insufficient evidence to reject the, uh, no insufficient evidence to reject the No. So, um, what that means is that we do not have enough evidence to claim that the, um, pace of life and gender are independent. So now with this, what is my recommendation? Um, I don't really know what a recommendation would be because each person's pace of life is their own. That is their own choosing. Um, so, yeah,

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:10

A normal population has a mean of $75 and standard deviation of$5. You s…

02:08

Engineers want to design seats in commercial aircraft so thatthey are wi…

07:03

Let X be normally distributed withmean μ = 19 and standarddeviation …

04:16

During a 20 year span, there were 133 major hurricanes in acertain area.…

14:02

Police estimate that 20% of drivers do not wear their seatbelts.They set…

Please provide answers of allquestions. As these are just MCQs, how…

02:44

3. Which of the following situations is modelled by a geometricdistribut…

02:56

Data from a sample of randomly selected students is shown below.The vari…