Week 5 Project – STAT 3001 – Chi-Square Goodness of Fit Test (equal frequencies)

| August 31, 2017

Question
Week 5 Project – STAT 3001
Student Name:

This assignment is worth a total of 60 points.
Part I. Chi-Square Goodness of Fit Test (equal frequencies)
In order to determine staffing levels, a hospital wants to determine if births occur with the same frequency
on each day of the week. The table below lists the days of the week selected by a random sample of 100
births. Consider the claim that the days of the week have the same frequency of a birth occurring.
Sunday
32

Monday
16

Tuesday
7

Wednesday
20

Thursday
11

Friday
8

Saturday
6

Instructions for performing this test in Stat Disk can be found in the Stat Disk User’s Manual under
Goodness of Fit, Equal Frequencies.
Instructions

Answers

1. Use the Chi-Square
Goodness-of-Fit test to see if
there is a difference between
the frequency of births and
days of the week. Use a
significance level of .01.
Paste results here.
2. What are we trying to show
here?
3. What is the p-value and what
does it represent in the
context of this problem?
4. State in your own words
what the results of this
Goodness-of-fit test tells us.
5. Repeat the above procedure
using only the weekdays
Paste results here. Did you
get different results? What
do they mean?

1

Part II. Chi-Square Goodness of Fit Test (unequal frequencies)
In the 2000 U.S. Census, the ages of individuals in a small town were found to be the following:
Less than 18 – 20%
18-35 – 30%
and
greater than 35 – 50%
In 2010 the ages of 500 individuals from the same small town were sampled with the following results:
Less than 18 – 121 people
18-35 – 288 people and
greater than 35 – 91 people
Using an alpha of 0.05, would you conclude that the population distribution of ages has changed in the
last 10 years? Instructions for performing this test in Stat Disk can be found in the Stat Disk User’s
Manual under Goodness of Fit, Unequal Frequencies.
Instructions

Answers

6. Complete the table as
necessary.
[Hint: You will need to compute
the observed frequencies based
on the percentages for the 500
samples. Round to the nearest
integer.]
7. Use the Chi-Square
Goodness-of-Fit test for
Unequal frequencies to see if
there is a difference between
the observed frequencies and
the expected frequencies Use
a significance level of .05.
Paste results here.
8. State the null and alternative
hypothesis.

Less than
18
121

OBSERVED

18-35
288

35-91
91

EXPECTED

9. What conclusion would you
reach, given the result of
your Goodness-of-Fit test?
[State in your own words
following the guidelines for a
conclusion statement learned
last week.]
Part III. Chi-Square Test of Independence
The following table is the result of a survey from a random sample of different crime victims.
Use the data to test the claim that the type of crime is independent of whether the criminal was a stranger.
Use a significance level of 0.05.

2

Criminal was a stranger
Criminal was an acquaintance
or relative

Homicid
e
12
39

Robbery

Assault

379
106

727
642

Hint: Instructions for performing this test in Stat Disk can be found in the Stat Disk User’s Manual under
the heading Chi Square Test of Independence (Contingency Tables).
Instructions

Answers

10. Just looking at the numbers in the
table, what is your best guess
about the relationship between
type of crime and criminal being a
stranger or not? Are they
independent or is there a
relationship?
11. Compute a Chi-Square Test of
Independence on this data using a
0.05 level of significance. Paste
your results here.
12. What are the null and alternative
hypothesis for this test?
13. What is the p-value for this result?
What does this represent?
14. State your conclusion related to the
context of this problem.

Part IV. Apply this to your own situation
Using one of the above statistical tests, compose and SOLVE an actual problem from the context of your
own personal or professional life. You will need to make up some data and describe which test you will
use to analyze the situation. Here’s an example:
Example: Do not use this problem!!
State the problem that you are
analyzing.
Make up some data for the new
situation.

Last year, I asked the kids in my neighborhood what
kind of cookies they preferred. 50% said chocolatechip, 20% said oatmeal-raisin, and 30% said sugar
cookie. I want to see if this has changed.
I asked 50 neighborhood kids what kind of cookie they
preferred now and here’s what they said:

35 said chocolate-chip
3

Determine which type of Chi-Square
test you will perform.
Specify your null and alternative
hypotheses.
Setup the test

5 said oatmeal-raisin
10 said sugar-cookie

Since these are unequal frequencies, I will perform a
Chi-Square Goodness-of-Fit Test (Unequal
Frequencies).
H0: There is no difference this year in the preferences
of cookies within the neighborhood kids.
H1: Things have changed.
Chocolate OatmealSugar-Chip
Raisin
Cookie
OBSERVED 35
5
10
EXPECTED 25

10

Perform the test

Paste your STATDISK results here

State your conclusion

15

We have evidence to believe ….

Submit your final draft of your Word file by going to Week 5, Project, and follow the directions under
Week 5 Assignment 2. Please use the naming convention "WK5Assgn2+first initial+last name" as the
Submission Title.

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