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 sentences. Make sure to

refer to the specific units of the variable AND the specific populatio