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Practice Problems

1) Read about the following experiment and fill in the blanks that follow.

Imagine a researcher wants to know the proportion of UCLA students who favor stricter immigration

regulations and whether immigration regulation preferences depend on an immigrant?s ethnicity. Imagine

that they also want embed an experiment in their survey where students read a vignette about either a

Latino, European, or unspecified immigrant prior to being asked about their immigration regulation

preferences.

a) Come up with at least one hypothesis that could be tested from this design?

b) What is the dependent variable?

c) What is the independent variable?

d) What are the experimental conditions?

e) What is the control group?

2) What are the main strategies of inquiry used in qualitative research? Provide a brief description

of each.

Below is a sample of 16 people from a recent survey and data about their age in years, highest level

of educational attainment and party identification (use for questions 8-10):

#

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Ag

e

41

58

62

68

33

52

50

28

31

24

22

48

71

18

78

36

Educational

Attainment

College

College

no High School

College

High School

College

no High School

High School

College

College

College

High School

no High School

High School

Party

Identification

Republican

Republican

Democrat

Republican

Republican

Democrat

Democrat

Republican

Democrat

Democrat

Republican

Democrat

Democrat

Democrat

Democrat

Republican

3) What is the measurement level of the Educational Attainment variable? What measure(s) of

central tendency can be calculated for this type of variable? Please calculate them.

Measurement level = ______________________________________

Measures of central tendency? ________________________________

For your calculations, use the space provided below.

4) Party identification is a nominal variable with two categories. Create a dummy variable

?Democrat? by assigning a {1} if a person identifies as a Democrat and a {0} if a person

identifies as a Republican. Use the table to below to create a frequency table. Next, calculate the

mean and standard deviation of this variable.

Party ID

f

Democrat (1)

Republican (0)

Total

%

5) Create a frequency table for Educational Attainment. Also calculate percentages and cumulative

frequencies and percentages. Use the table below.

Education

f

%

cf

c%

Total

6) Create a bar graph for Educational Attainment. (Note: If you make the graph using word, or any

of the Microsoft Office programs, go to ?insert? and then ?chart.? For a bar graph you use the

clustered column option. An excel spreadsheet will pop up that you can enter the data into. Play

around with it until it looks right.)

7)

Below is data on the population density (i.e. inhabitants per square mile) for ten selected

(assume randomly sampled) U.S. states. Calculate the mean and standard deviation (s) for

this sample. Use the table below to help keep track of your calculations.

state

Connecticut

Indiana

Kansas

Kentucky

Massachusetts

Michigan

Mississippi

New York

Oklahoma

8)

populatio

n density

1

738

181

34

109

835

174

63

411

54

x-xbar

(x-xbar)^2

In your words, describe what a standard deviation is.

9) Which measure of central tendency would you likely use if you had a highly skewed distribution?

a) Mode

b) Median

c) Mean

10) The greater the variability around the mean of a distribution, the larger the

a) Range

b) standard deviation

c) variance

d) All of the above.

11) The relative likelihood of occurrence of any given event is known as that event?s

a) standard deviation.

b) area under the normal curve.

c) probability.

d) All of the above.

12) A probability distribution is based on

a) actual observations.

b) probability theory.

c) the Central Limit Theorem.

d) the subtraction rule.

13) A Veterinarian tells you that the measured heart rate in healthy dogs is normally distributed and most

dogs (about 95%) have a heart rate between 60 and 160 beats per minute. What are the mean and standard

deviation of measured heart rate in dogs?

14) The inevitable difference between the mean of a sample and the mean of a population based on

chance alone is a

a) random sample.

b) condence interval.

c) sampling error.

d) probability.

15) What percent of a standard normal distribution N(? = 0, ? = 1) is found in each

region? Be

sure to draw a graph, shading the area you?re looking for.

a) Z &gt; ?1.2

b) |Z| &gt; 1.96

16) The average income of recent UCLA graduates is \$45,600. You are interested whether alumni

who majored in political science earn more or less than the overall average, and contact 30

recent, randomly chosen political science graduates and ask them about their earnings. The

mean income in your sample is \$ 37,350, the sample standard deviation is \$22,500. Calculate

a 95% confidence interval around your mean. Does the confidence interval include the overall

school average? What does this tell us? (Note: This is a fairly small sample size, so use the

t-distribution. Oh, and the data for political science graduates is made up.)

17) The Scholastic Assessment Test (SAT) is standardized to have a population mean ? = 500. Suppose a

researcher gives the SAT to a random sample of 60 students at a private high school, yielding a sample

mean of 541, and sample standard deviation of 105. Based on this sample, can this researcher conclude

that this private school?s students have higher SAT scores than the average student?

a) What type of hypothesis test would you use to test whether private school students have higher

SAT scores than the regular population of SAT takers?

b) Using the SAT information, test the null hypothesis that the private school students do not have

higher SAT scores using a two-tailed t-test at significance level of ? = .05. Make sure you follow

hypothesis testing steps you learned in class.

18) What is Type I error? What is Type II error?

19) Suppose that an emergency room doctor is interested in the relationship between gender, age, and

sensitivity to pain among adult patients. She collects from a sample of 57 hospital files the information

on patients? self-reported pain scores, ranging from 0 for no discomfort to 10 for the worst pain

imaginable, along with the patients? ages in years and gender (1 for male and 0 for female). The results of

her regression analysis predicting pain based on age and gender are shown in the following table:

Variable

Constant (a)

Age

Gender

N

Coefficient

1.321

0.065

0.857

57

SE

0.239

0.041

0.665

t

5.527

1.585

1.289

a) Write out the regression equation for this analysis.

b) Interpret the constant (Y-intercept).

c) Interpret the regression coefficients for age and gender.

d) Indicate which, if either, of the two independent variables is a significant predictor of pain

score. How do you know?

Bonus!

20) Calculate the mean and standard deviation (s) for Age given in the first table.

Bonus bonus!

21) What are nuisance variables in experiments? What are the effects of nuisance variables in

experiments?

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