STAT 110: Homework 4 Solutions (20 pts)
Spring 2017
1. Suppose the Fish and Game Department stocked a particular man-made lake with fish in the
following proportions: 30% catfish, 15% bass, 40% bluegill, and 15% pike. Five years later, it
sampled the lake to see if the distribution of fish had changed. It found that the 500 fish in the
sample were distributed as follows:
Type
Catfish
Bass
Bluegill
Pike
Total
Frequency
128
84
216
72
500
Research Question: Is there evidence that the distribution of fish has changed from five years ago?
a. Write the null and alternative hypotheses for investigating this research question. (2 pts)
Ho: the distribution of fish has not changed from five years ago
(πcatfish = 0.30, πbass = 0.15, πbluegill = 0.40, πpike = 0.15)
Ha: the distribution of fish has changed from five years ago
b. How many of the 500 fish do we expect to see of each type if the distribution of fish in the lake
has not changed? Show your work to justify your answer (don’t forget to do this for each type
of fish). (2 pts)
Catfish: 30% of 500 = 150
Bass: 15% of 500 = 75
Bluegill: 40% of 500 = 200
Pike: 15% of 500 = 75
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c. Find the chi-square test statistic for investigating this research question by hand. Show your
work to receive full credit. (2 pts)

 (Observed - Expected 
128  1502  84 - 752  216 - 2002  72 - 752 = 5.707

 
Expected
150
75
200
75


2
d. Carry out the chi-square test in JMP, and find the p-value for investigating this research
question (you should attach your JMP output to receive full credit). (2 pts)
p-value: 0.1268
Common Error: JMP alphabetizes the categories! If you just list the hypothesized
proportions in the order described, you get the wrong result (shown below).
e. Write a conclusion in the context of the research question. (2 pts)
The data do not provide enough evidence to conclude that the distribution of fish has
changed in this lake from five years ago.
2
2. According to the “2015 Crash Facts” reported by the Minnesota Department of Public Safety, the
following number of alcohol-related crashes occurred on each given day of the week in the state of
Minnesota in 2015.
Source: https://dps.mn.gov/divisions/ots/reports-statistics/Documents/2015%20Crash%20Facts.pdf
Day of the week
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Total
Frequency
714
345
375
382
424
583
811
3,634
Research Question: Is there evidence that alcohol-related crashes are more likely to occur on some
day(s) of the week than on others?
a. Write the null and alternative hypotheses for investigating this research question. (2 pts)
Ho: Alcohol-related crashes are equally likely to occur on any given day of the week
(πSunday = πMonday = πTuesday = πWednesday = πThursday = πFriday = πSaturday = 1/7 = 14.286%)
Ha: Alcohol-related crashes are not equally likely to occur on any given day of the week
b. How many of the 3,634 crashes do we expect to see on each day of the week if alcohol-related
crashes are equally likely to occur each day? Show your work to justify your answer. (2 pts)
1/7 of 3634 = 519.14
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c. Find the chi-square test statistic for investigating this research question by hand. Show your
work to receive full credit. (2 pts)

 (Observed - Expected 
714  519.142  345  519.142  375  519.142

 
Expected
519.14
519.14
519.14


2
2
2
2
2




382  519.14
424  519.14
583  519.14
811  519.14




519.14
519.14
519.14
519.14
 397.2
d. Carry out the chi-square test in JMP, and find the p-value for investigating this research
question (you should attach your JMP output to receive full credit). (2 pts)
p-value: < 0.0001
e. Write a conclusion in the context of the research question. (2 pts)
The data provide statistical evidence that alcohol-related crashes are not equally likely to
occur on any given day of the week. It appears that more are happening on the weekends.
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