For

Assignment 4:

Part 1: Handwritten

Part 1. A

Three different sections of the same Interstate highway, with roughly equal traffic volumes, have been patrolled by the State Police at varying intensity levels for the past six months. The posted speed limit is

55

, and the speeds of a random sample of motorists have been registered for each of the three sections. Is there any statistically significant difference in the speeds? Use the 5/6 step model as a guide, write a short paragraph interpreting your results. (I want to see all 5/6 steps and descriptive statistics in your interpretation. Make sure to show all work.)

58

58

55

58

55

55

58

55

65

54

55

Lightly Patrolled |
Moderately Patrolled |
Heavily Patrolled |
|||||

55 |
57 |
50 |
|||||

48 |
58 |
51 |
|||||

60 |
|||||||

65 |
|||||||

72 |
|||||||

67 |
59 |
52 |
|||||

54 |
|||||||

Part 1. B

The city council is considering a law prohibiting smoking in all public facilities. A sample has been selected from the community and tested for support of the ordinance. Is there a statistically significant relationship between age and support for the anti-smoking law? Use the 5/6 step model as a guide, write a short paragraph interpreting your results. (I want to see all 5/6 steps and descriptive statistics in your interpretation. Make sure to show all work)

Age |
|||||||||

Less than 40 |
More than 40 |
||||||||

Support: |
For |
145 |
78 |
223 |
|||||

Against |
103 |
169 |
272 |
||||||

248 |
247 |
495 |

Please submit your answers to part 1 via a word document and any handwritten work that needs to be shown via a PDF to the assignment folder.

Part 2. Part two is an SPSS assignment.

Using the SPSS data set created for the first assignment, test the following hypothesis using the 5/6-step module as a guide and write a short paragraph about your findings for each hypothesis. Finally, please submit your answers for each question (showing all 5/6 steps) via a word document and copy your SPSS output for each hypothesis via an SPSS file. (It can be assumed that the data meet the assumptions of random sampling, independence, and a normal distribution. If other assumptions are violated, you will need to recode to meet assumptions.)

Test the following hypothesis:

· The sample population’s GPA is significantly lower than the national average.

· (National average= 2.5)

· There is a significant difference between race and people’s feelings about legalizing marijuana.

· (Hint: To meet assumptions, you must recode the variables. So please remember to always recode into a new variable.)

· There is a significant difference in the number of partners between males and females.

· There is not a significant difference between race and age when Freshman.

· If there is a significant difference, which race significantly differs from the others? Why is this important?

Please submit your answers to the assignment folder by the end of the learning module. Assignments scoring above a 30% Turnitin.com rating are subject to a point reduction. Assignments scoring above a 40% Trunitin.com rating will receive a zero on the assignment for originality, not for plagiarism. Keep direct quotes to a minimum.

Make sure to use APA format for in-text citations and references.

Okay, so for this video, we are going to be going over that assignment for the first part of assignment four is 18 and says this is where you’ll be physically doing the statistics by hand. And so for the first when we will be doing an ANOVA. And so make sure that you show your work. I’m specifically going to be looking for making sure that you find your sum of squares within and total in-between and of course your F value and where your cutoffs are. So make sure that you write everything up using The five or six step model as a guide. So for B, we will actually be using Chi-square. So again, just make sure that you got there all the steps and show your work. So part 2 is a section that your book doesn’t really go over a whole lot that I wanted to go over it. Say for the first one, we have first hypothesis as a sample calculations, number of partners is significantly lower than the national average. And so in order to do this right here, we see that we have to compare means. And we know the mean of the sample population or the actual population versus the sample population. And so if we want to compare the sample population to the actual population, we will go into our SPSS data 10. So let’s say that we’ll use legalization as an example. And so I wanted to know our average was close to the nation’s average for legalization. Then I will go to Compare Means and then a one-sample t-test. And so here we go. I need to find my legalization, the area. All right, and let’s say that the national average is somewhere in between. So we’ll pick five. And so every run a test, and it gives us the mean. And let’s see if we are statistically different. So now we are not statistically different when it comes to if that was the nation’s average. We’re actually running a sample, a comparison. Okay, so that’s how you would do the first one. So let’s go back over and see what the second one says study. So there is a significant difference between raised and how people feel about legalizing marijuana. And so in order to do this, we see that we have to grant categorical variables. So we have race and this nominal and our other variable, it is or not. And so we would have to do a chi-square test. And so if we go back over here and we look at our data, and we wanted, you do, let’s say race and legal. Now, Let’s pull this back up. And remember that when the assumptions are the chi-squared is that you need to have an expected value. At least 80 percent or more of your frequencies are greater than or equal to five. And so let’s say if we just went ahead and ran it straight as it’s asking for right now. And so we would go to analyze descriptives and then cross tabs. And so they were still even race and legalization the way it is. And so for this statistics, we want to make sure that the chi-squared box is continued. And then for these, I was like, you see the observed and we need the expected rate. Otherwise we can’t test score, but it is a return to test for. And then I always like to see these as well. And so if I hit Continue here, and then okay, and then, wow, this is really hard to interpret, right? And if we go all the way down here, we see that 60 percent of the cells actually says a 100 percent have excitation counts less than five. And so this is all kinds assumption violations. And so this data that’s Iran, it is pretty much useless. And so what you need to do. Is go in and take these two variables and break them down in a way that you do have 80 percent or more at the expected values which are about 55 or above. And so in order to do that, we go back to our dataset. And I want to go to Transform. And then you always want to recode into a different variable. And so let’s say that I did want to recode race. And well, I would click on brace and move it over. And then you can call it whatever you want. So I’m going to call this line, raise the senses, the video example. And I want to click on here. Alright, and so let’s say that I want my groupings to be bites. And I still just wanted to keep the whites the same hierarchy. By 01:00 AM I went to this way, I had a coded in there. And then maybe I want to combine my Hispanics and African-Americans, right? And so that’s my 23. So I will go back over here and I will put my 2233. And so that would now be coded as a two. And then out at, and then maybe I just want to include all of the others. And there, and all the other variables would be three. And then add and then go to Continue and then hit Change. And then okay. And so now if we go over to our data set, we will see that the new variable should be over here. And there is our new variable for race and video. And so you guys can see it. And looking at it, I did several recordings to make extra sure that I had the best one. So you’re going to want to play around with it, find out which one it is. And so I’ll give you a hint that you will have to dichotomize the variables in order to meet that assumption. And one thing that I highly suggest for you to do is look at the descriptives for those two variables. So remember how you do that, descriptives. And so let’s say that I want to look at race. And they don’t need any of that stuff for this one, I’m just wondering about the camp actually. And so how could I dichotomize the fats? And so you might have to play around with it. That one of the things that you want to remember is that you need to have a logical reason for how you break them down and how you combine them. But looking at this kinda helps give us idea to you. Keep it even ends. So essentially, we’re looking for five in each category. So you would need roughly and at least that you could get five in each category. And that’s why you have to dichotomize it. Alright? When we have a dichotomous variable and a interval ratio variable. And so that would be a different t-test here. And so let’s say that we wanted to go back to our data here and recline to work at it. Right now. Go ahead and leave my gender. So gender in there, and pick a different on that. So here we go back to compare means. I’m going to connect. Here we go, and then here we’re doing a independent sample t-test. And so our group is gender. And for this one, let’s add, I’m going to look at racial prejudice and see how it turns out. So I would move that into that category there. And say for gender, I do have two primary groups. And so I have them coded as one for male and female. And I’ve gotta make sure to write down the numbers are just separate them out. And then I go, Okay? And so here is what the output would look like. And so what we’re looking for is if there is a equal variance assumption or not. And so that’s what Levene’s test is all about. And so Levene’s test is equal variances assumed if it’s greater than 0.05 and it’s not assumed equal if p is less than point of five. So P is less than 15. So we would have to use this bottom one here and say No, it is significant at the 0.05 level. And so that’s how you would go about doing that particular one, the way you need to use the variables that are indicated. Right? And so for the fourth one, we have that there is not a significant difference between race and age within freshmen. So a turnover, they first started their freshman year. And so this fun, we have a categorical independent variable and a interval ratio dependent variable. So when we have that, we need to use an ANOVA. And so we also need to make sure that we have at least three groupings. And so I am going to look at, and he is 13 groupings that I’ve already created. So I want to compare means one-way ANOVA. And when they have that is broken into three points. I want to get rid of it. Actually, we can leave that way. I don’t want to because that’s going to look crazy. All right. Let’s do you do You had have you whatever you guys are looking at. You guys are looking at race and age a freshman. So I’m going to give me number apart errors. And let’s go with that. One day I have three categories. And so let me see how about this one had three? Does not. And so when it does the police act, you want to hit Post hogged And they bear frowny. And so that’s going to allow you to answer the second part of the question. And so here we go. Yes to pick one has three. All right, and so overall our F-test, but not significant. And so if we go over here, then we could look at, I’ve said these, I broke down into people who do not support legalization of marijuana. People who are kind of neutral about legalization of marijuana, and people who do support it. And so that’s the way I burgers and there’s three categories using the case. I can’t do it from the stamp the way that I just showed you how to recode variables earlier. And so here, we would look at these and see if there’s a difference between each of them. And so it wasn’t significant and this example that in your example it may or may not be. And so remember that you probably should try and keep it simple. I would probably if I was you look at race from a broken endpoint and 23. And so logically how you would split up debris. And remember that one of the assumptions for ANOVA is that they are roughly equal categories. And you want to figure out a way where you can break, raise up into three roughly equal groups based on logic and reason. And so once you did that, you’d like to see if it’s in if it’s significantly different or not. And then you want to test to see which one is significantly different. And then speculate about why that might be. And say you might see more than one being statistically different than the others. And so again, just make sure that you are following the five or six that process. So I always do the six steps just because that’s the way I was taught. So in your video lectures and the PowerPoint that’s posted for this module goes over six steps instead of five. But really if you want to do the five, it’s okay. And so that is how you do the assignment for this one.

one-tail area 0.250 0.125 0.100 0.075 0.050 0.025 0.010 0.005 0.000

5

two-tail area 0.500 0.250 0.200 0.150 0.100 0.050 0.020 0.010 0.00

10

d.f. c 0.500 0.750 0.800 0.850 0.900 0.950 0.980 0.990 0.99

9

1

2

3

4

5

1.000 2.414 3.078 4.165 6.314 12.706 31.821 63.657 636.6

19

0.816 1.604 1.886 2.282 2.920 4.303 6.965 9.925 31.599

0.765 1.423 1.638 1.924 2.353 3.182 4.541 5.841 12.9

24

0.741 1.344 1.533 1.778 2.132 2.776 3.747 4.604 8.610

0.727 1.301 1.476 1.699 2.015 2.571 3.365 4.032 6.869

6

7

8

9

10

0.718 1.273 1.440 1.650 1.943 2.447 3.143 3.707 5.959

0.711 1.254 1.415 1.617 1.895 2.365 2.998 3.499 5.408

0.706 1.240 1.397 1.592 1.860 2.306 2.896 3.355 5.041

0.703 1.230 1.383 1.574 1.833 2.262 2.821 3.250 4.781

0.700 1.221 1.372 1.559 1.812 2.228 2.764 3.169 4.587

11

12

13

14

15

0.697 1.214 1.363 1.548 1.796 2.201 2.718 3.106 4.437

0.695 1.209 1.356 1.538 1.782 2.179 2.681 3.055 4.3

18

0.694 1.204 1.350 1.530 1.771 2.160 2.650 3.012 4.2

21

0.692 1.200 1.345 1.523 1.761 2.145 2.624 2.977 4.1

40

0.691 1.197 1.341 1.517 1.753 2.131 2.602 2.947 4.073

16

17

18

19

20

0.690 1.194 1.337 1.512 1.746 2.120 2.583 2.921 4.015

0.689 1.191 1.333 1.508 1.740 2.110 2.567 2.898 3.965

0.688 1.189 1.330 1.504 1.734 2.101 2.552 2.878 3.9

22

0.688 1.187 1.328 1.500 1.729 2.093 2.539 2.861 3.883

0.687 1.185 1.325 1.497 1.725 2.086 2.528 2.845 3.8

50

21

22

23

24

25

0.686 1.183 1.323 1.494 1.721 2.080 2.518 2.831 3.819

0.686 1.182 1.321 1.492 1.717 2.074 2.508 2.819 3.792

0.685 1.180 1.319 1.489 1.714 2.069 2.500 2.807 3.768

0.685 1.179 1.318 1.487 1.711 2.064 2.492 2.797 3.7

45

0.684 1.198 1.316 1.485 1.708 2.060 2.485 2.787 3.725

26

27

28

29

30

0.684 1.177 1.315 1.483 1.706 2.056 2.479 2.779 3.707

0.684 1.176 1.314 1.482 1.703 2.052 2.473 2.771 3.690

0.683 1.175 1.313 1.480 1.701 2.048 2.467 2.763 3.674

0.683 1.174 1.311 1.479 1.699 2.045 2.462 2.756 3.659

0.683 1.173 1.310 1.477 1.697 2.042 2.457 2.750 3.646

35

40

45

50

60

0.682 1.170 1.306 1.472 1.690 2.030 2.438 2.724 3.591

0.681 1.167 1.303 1.468 1.684 2.021 2.423 2.704 3.551

0.680 1.165 1.301 1.465 1.679 2.014 2.412 2.690 3.520

0.679 1.164 1.299 1.462 1.676 2.009 2.403 2.678 3.496

0.679 1.162 1.296 1.458 1.671 2.000 2.390 2.660 3.460

70

80

100

500

1000

0.678 1.160 1.294 1.456 1.667 1.994 2.381 2.648 3.435

0.678 1.159 1.292 1.453 1.664 1.990 2.374 2.639 3.416

0.677 1.157 1.290 1.451 1.660 1.984 2.364 2.626 3.390

0.675 1.152 1.283 1.442 1.648 1.965 2.334 2.586 3.310

0.675 1.151 1.282 1.441 1.646 1.962 2.330 2.581 3.300

00

0.674 1.150 1.282 1.440 1.645 1.960 2.326 2.576 3.291

c is a confidence level

Critical Values for Student’s t Distribution

Area c

–t 0 t

One-tail area

Right-tail

area

0 t

Left-tail

area

–t 0

Two-tail area

Area

–t 0 t

For degrees of freedom d.f. not in the table, use the closest d.f. that is smaller.