AP Statistics
Review: Chi-Square
Name ______________________________________
Part I. Perform the following tests.
1.
A study is being conducted to determine whether there is a relationship between jogging and blood
pressure. A random sample of 210 subjects is selected, and they are classified as shown in the table. At
 = 0.05, test the claim that jogging and blood pressure are not related.
Jogging Status
Joggers
Non-joggers
Low
34
15
Blood Pressure
Moderate
High
57
21
63
20
2. A staff member of an emergency medical service wishes to determine whether the number of accidents is
equally distributed during the week. A week was selected at random, and the following data were obtained.
Is there evidence to reject the hypothesis that the number of accidents is equally distributed throughout
the week, at  = 0.05?
Day
Mon.
# accidents
28
Tues.
32
Wed.
15
Thurs.
14
Fri.
38
Sat.
43
Sun
19
3. Shopping at secondhand stores is becoming more popular and has even attracted the attention of business
schools. A study of customers’ attitudes toward secondhand stores interviewed samples of shoppers at two
secondhand store of the same chain in two cities. The breakdown of the respondents by sex is shown below.
Is there a significant difference between the proportions of women customers in the two cities?
Men
Women
City A
38
203
City B
68
150
4. The chair of the history department of a college hypothesizes that the final grades are distributed as 40%
A's, 30% B's, 20% C's, 5% D's and 5% F's. At the end of the semester, the following numbers of grades
were earned. For  = 0.05, is the grade distribution for the department different from that expected?
Grade
Number
A
45
B
52
C
39
D
8
F
6
5. A survey of the 164 state representatives is conducted to see whether their opinions on a bill are related to
their party affiliation. The following data are obtained. At  = 0.01, can the researcher conclude that
opinions are related to party affiliations?
Party
Republican
Democrat
Independent
Opinion
Approve Disapprove No opinion
27
15
13
43
18
12
9
15
12
Part II. Identify the type of chi-square test shown below and state the hypotheses.
6. The concessions manager at Twin Rivers Stadium wishes to see whether there is any preference in the
flavors of popcorn that are sold during sporting events. A random sample of sales is selected, and the data
are shown below. At  = 0.01, are the flavors selected with equal frequency?
Flavor
# sold
Plain
25
Barbecue
18
Butter
32
Cheddar
45
7. A recent Gallup poll asked the same question that has been asked every year for many years: “What do you
think is the most important problem facing this country today?” The responses are shown below for the
three major concerns over the years 1995 to 1998. Are the proportions for the problems the same for each
year?
1998
1997
1996
1995
Jobs
110
180
200
210
Crime
200
200
250
250
Health Care
60
60
80
70
Other
630
560
470
470
8. A researcher wishes to determine if on-line service or Internet use is independent of user. A sample of 300
computer users shows the following data. At  = 0.10, can the researcher conclude that usage is independent
of the user?
Business
Consumer
Service Usage
Increase
Same
79
21
122
63
Decrease
10
15
9. The American Red Cross reports that 42% of Americans have type 0 blood, 44% have type A blood, 10% have
type B blood, and 4% have type AB blood. A county medical examiner hypothesizes the distribution of blood
types is the same in his county as it is nationally. A random sample of 200 people is selected, and the
following data are tallied. At  = 0.10, can the examiner conclude that his hypothesis is correct?
Type
Frequency
O
58
A
65
B
55
AB
22
10. A children's playground equipment manufacturer read in a survey that 55% of all American playground
injuries occur on the monkey bars. The manufacturer wishes to investigate playground injuries in four
different parts of the country to determine if the proportions of accidents on the monkey bars are equal.
The results from randomly selected samples are shown below. At  = 0.01, test the claim that the
proportions are equal.
On Monkey Bars
Not on Monkey Bars
North
South
East
West
15
15
30
18
12
30
13
17
30
16
14
30
Part III. For each of the following, state the formula that you would use. If it’s a hypothesis test give the hypotheses and
state the value of the test statistic and p-value. If it’s a confidence interval then state the interval.
11. A telephone company representative estimates that 40% of its customers want call-waiting. To test this hypothesis, she
selected a sample of 250 customers and found that 37% had call waiting. At a 1% significance, is her estimate
appropriate?
12. If you bought a used camera in good condition from a friend, would you pay the same as you would if you bought the
same item from a stranger?
Friend
Stranger
275
260
300
250
260
170
300
130
255
200
275
225
290
240
13. A sample of 35 assistant professors had a mean salary of $43,260 with a standard deviation of $5230 and 40 professors
had a mean salary of $65,870 with a standard deviation of $5890. Find a 99% confidence interval for the mean
difference in the salaries of assistant professors and professors.
14. In a sample of 80 Americans, 62 wished that they were rich. In a sample of 90 Europeans, 56 wished that they were
rich. Find and interpret the 95% confidence interval for the difference of the two proportions.
15. A researcher wishes to estimate the average age of lifeguards is Ocean City. She selects a sample of 26 guards and
finds the mean of the sample to be 24.7, with a standard deviation of 2 years. Find a 95% confidence interval.
16. The AMA wants to test the idea that general practitioners are more in favor of government controlled health care
reform. In a sample of 200 surgeons, they found that 15% thought the government should control health care. In a
sample of 200 general practitioners, 21% felt this way.
17. A dietitian wishes to see if a person’s cholesterol level will change if the diet is supplemented by a mineral. Can it be
concluded that the cholesterol level has changed? Construct a 90% confidence interval.
Subject
1
2
3
4
5
6
Before
210
235
208
190
172
244
After
190
170
210
188
173
228
18. The Medical Rehabilitation Foundation reports that the average cost of rehabilitation for stroke victims is $24,672. To
see if the average cost of rehabilitation is different at a large hospital, a researcher selected a random sample of 35
stroke victims and found that the average cost of their rehabilitation is $25,266. The standard deviation is $3,251.
Use a 1% significance level.