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Sociology 3000

Social Statistics

Spring 2021

Exam 3

Instructions: Please thoroughly read all of the instructions in the questions (some have detailed

instructions). You have until Friday the 16

th

of April t 11:59 to complete the exam. The

individual point values for each question are listed. The entire exam is worth 150 points.

*Please Show ALL WORK for partial credit

Name:__________________________________________________

1. The table below shows the mean years of education for a sample of respondents for the 2014

General Social Survey (GSS) by their socioeconomic class. Use the table to answer questions 1a-

1d

[25 points]

Class

Mean

Standard deviation

N (sample size)

Working class

13.01

2.91

541

Middle class

14.99

2.93

475

Upper class

15.44

2.83

34

a. Calculate a 95% confidence interval for the mean number of years of education for working

class respondents

(be sure to include units).

b. Calculate a 95% confidence interval for the mean number of years of education for middle

class respondents (be sure to include units).

c. Calculate a 95% confidence interval for the mean number of years of education for upper class

respondents (be sure to include units).

d. What conclusions can you make about the differences in years of schooling for working,

middle, and upper class folks? Are they significantly difference (*hint: make sure you are

looking at your confidence interval for the three groups and comparing themdo they cross

over? Can we conclude with 95% confidence that the means are truly different?)

2. Researchers for the American Communities Survey (ACS) found that the mean income for

families in Valdosta, Georgia in 2018 was

$56,144 a year (US average is $87,864 a year) with a

standard deviation of $5,859 using a sample of 212 people in Valdosta. (data: 2018 ACS)

[20

points]

a. Calculate a 99% confidence interval for the mean annual income for people living in Valdosta,

Georgia.

b.

Interpret your results (make sure to include the units of analysis and a reference to the

population).

Please answer in one/two sentence(s).

c. Consider that the 2018 ACS found that the median income in Valdosta, GA is $32,051. Why is

this estimate so much lower, and what are the issues with mean income (hint, think about the

differences between the mean and median, and how these family size can impact the

mean/median)?

3. According to the U.S. department of transportation, there is a mean of 1.97 vehicles per

household in the U.S with a standard deviation of 0.35 (population parameters). A transportation

researcher has hypothesized that people with a college degree (or higher) in environmental

sciences are less likely to drive a car than people without higher education degrees in

environmental sciences because they tend to be more environmentally conscious. Using a

random sample of 650 people in the U.S. with a degree in environmental sciences, the researcher

found that the mean number of vehicles per household was 1.69 with a standard deviation of

0.18. Perform a hypothesis test to determine whether there is a difference between the mean

number of vehicles owned by all Americans, and the mean number of vehicles owned by people

with a college degree or higher in environmental sciences.

(hint: this is the first of three types of hypothesis testing, a population with known parameters

vs. a specific group. Use a Z-distribution)

[35 points]

a.

What assumptions must you make when performing a hypothesis test to compare a

sample mean to a population mean? (Three assumptions). And, what do these

assumptions tell us (in other words, why make these assumptions)?

b.

Fill in the values for the following variables:

=

=

X =

N =

c.

State your research and null hypotheses using a

one-tailed test

(note that the researcher

has a theoretical reason for using a one-tailed test).

d.

Using = 0.05 (a 95% confidence level)

compute the test statistic

using a Z-distribution

(as our population standard deviation is known).

e.

What can you conclude about your hypothesis (reject or fail to reject the null)? Interpret

your result in two sentences. Make sure to refer to the specific units of the variable AND

the specific population.

4. According to the University Admissions website, Valdosta State undergraduate students have

an average High School GPA of 3.13 on a 4.0 scale. Interested in group differences, a researcher

wants to focus on differences in high school GPA within different majors at

Valdosta

State. First,

the researcher took a sample of 65 undergraduate students majoring in sociology at

Valdosta

State and found that the average high school GPA among this sample group was 3.48 with a

standard deviation of 0.32. Then, the researcher took a sample (which was selected

independently of the first sample) of 85 undergraduate students majoring in marketing and found

that the mean GPA for this group is 3.55 with a standard deviation of 0.23. Test for differences

in mean high school GPA between sociology and marketing majors using a hypothesis test.

Assume both samples were randomly and independently selected.

(hint: this is the second of three types of hypothesis testing, comparing two group means with

unknown parameters. Use a t-distribution)

[35 points]

a.

What assumptions must you make when performing a hypothesis test to compare two

group means? (Four assumptions). And, what do these assumptions tell us (in other

words, why make these assumptions)?

b.

Fill in the values for the following variables:

Group 1 (Sociology Majors)

Group 2 (Marketing Majors)

N

1

=

N

2

=

X

1

=

X

2

=

S

1

=

S

2

=

df

1

=

df

2

=

df

total

=

c.

State your research and null hypotheses using a

two-tailed test

.

d.

Using = 0.05 (a 95% confidence level)

compute the test statistic

using a t-distribution

(as our population standard deviation is unknown).

e.

What can you conclude about your hypothesis (reject or fail to reject the null)? Are the

high school GPA's of Valdosta State sociology majors different than the high school

GPA's of marketing majors at VSU? Interpret your result in two sentence