OPMT 1197
Business Statistics
Lecture 20: Chi-Square Test for Independence
1. In 2009, the Physicians for a Smoke-Free Canada conducted a study of tobacco use in
British Columbia. They computed the smoking rates for men and women between the ages
of 20 and 34. The table below shows the number of smokers (daily and occasional) by
gender for a random sample of 500 British Columbians aged 20 to 34.
Smoke?
Yes No Total
Men 50 150 200
Women 55 245 300
Total 105 395 500
(a) At the 5% level of significance, is there enough evidence to conclude the smoking rates are
different for men and women? (i.e. to conclude that smoking depends on gender?)
(b) Could you reject H0 at the 10% level of significance? Estimate the p-value.
2. There are three types of beer: light, regular, and dark. The question is asked as to whether
women have the same preferences for the three types of beer as men. If the preference for
beer depends on the sex of the beer drinker then the marketing campaign will be revised to
target different markets. A test of independence answers the question: Is beer preference
(light, regular, or dark) independent of the sex of the beer drinker?
Is there enough evidence to conclude that beer preference depends on the sex of the beer
drinker? Test the hypothesis at the 5% level of significance.
Sample Results for Beer Preference of Male and Female Beer Drinkers (Observed Frequencies)
Beer Preference
Light Regular Dark Total
Male 20 40 20 80
Female 30 30 10 70
Total 50 70 30 150
Lab Exercises: Textbook Reading 12.3
1. A study was conducted to determine whether the preference for a two-wheel drive or a four-
wheel drive automobile is related to the gender of the purchaser. A sample of 90 buyers was
selected, and the data are as shown in the table. At the 5% level of significance, can the
researcher conclude that the automobile preference depends on the gender of the buyer?
Your test must include H0/HA, a decision with justification and a conclusion.
2-Wheel Drive 4-Wheel Drive Total
Male 23 43 66
Female 18 6 24
Total 41 49 90
Pg 1 of 5
, OPMT 1197
Business Statistics
2. In a survey involving 200 cars, each vehicle was classified according to whether or not it had
antilock brakes and whether or not it had been involved in an accident in the past year.
Antilock Brakes?
Accident? Yes No Total
Yes 9 11 20
No 141 39 180
Total 150 50 200
(a) What percentage of cars had been involved in an accident in the past year?
(b) What percentage of cars with antilock brakes had been in an accident in the past year?
(c) What percentage of cars without antilock brakes had been in an accident in the past year?
(d) Based on your answers above, do antilock brakes seem to help reduce the accident rate?
(does whether or not a car is in an accident depend on whether it had antilock brakes?)
(e) Does the data provide sufficient evidence that the accident rate for cars with antilock
differs from those without antilock brakes? Test at the 1% level of significance.
3. The Provincial government is considering implementing a new anti-smoking law which
would ban smoking in apartments and hotel rooms. They want to see if men hold the same
opinion on the proposed smoking ban as women. 500 randomly selected British Columbians
are cross-classified by their sex and opinion on the smoking ban. The results are below:
Opinion of the Smoking Ban
Gender Against Neutral In Favour Total
Male 71 36 133 240
Female 54 39 167 260
Total 125 75 300 500
(a) Is there enough evidence to conclude that men's opinions on the smoking ban differ
significantly from women's opinions? Test at the 5% level of significance. Your test
must include H0/HA, a decision with justification and a conclusion.
(b) Estimate the P-value
4. You own a store that sells household appliances. You make a very good margin selling
extended warranties on appliances. You want to investigate who buys these and so you take
a sample of 110 customers. You estimate their ages and obtain the following data about who
buys or doesn't buy the extended warranty.
Under 30 30 to 50 Over 50 Total
Buy 15 33 18 66
Did Not Buy 18 22 4 44
Total 33 55 22 110
You wish to see if customers of different ages respond differently when you offer to sell
them an extended warranty. Test the hypothesis at the 5% level of significance. Your test
must include H0/HA, a decision with justification and a conclusion.
Pg 2 of 5
Business Statistics
Lecture 20: Chi-Square Test for Independence
1. In 2009, the Physicians for a Smoke-Free Canada conducted a study of tobacco use in
British Columbia. They computed the smoking rates for men and women between the ages
of 20 and 34. The table below shows the number of smokers (daily and occasional) by
gender for a random sample of 500 British Columbians aged 20 to 34.
Smoke?
Yes No Total
Men 50 150 200
Women 55 245 300
Total 105 395 500
(a) At the 5% level of significance, is there enough evidence to conclude the smoking rates are
different for men and women? (i.e. to conclude that smoking depends on gender?)
(b) Could you reject H0 at the 10% level of significance? Estimate the p-value.
2. There are three types of beer: light, regular, and dark. The question is asked as to whether
women have the same preferences for the three types of beer as men. If the preference for
beer depends on the sex of the beer drinker then the marketing campaign will be revised to
target different markets. A test of independence answers the question: Is beer preference
(light, regular, or dark) independent of the sex of the beer drinker?
Is there enough evidence to conclude that beer preference depends on the sex of the beer
drinker? Test the hypothesis at the 5% level of significance.
Sample Results for Beer Preference of Male and Female Beer Drinkers (Observed Frequencies)
Beer Preference
Light Regular Dark Total
Male 20 40 20 80
Female 30 30 10 70
Total 50 70 30 150
Lab Exercises: Textbook Reading 12.3
1. A study was conducted to determine whether the preference for a two-wheel drive or a four-
wheel drive automobile is related to the gender of the purchaser. A sample of 90 buyers was
selected, and the data are as shown in the table. At the 5% level of significance, can the
researcher conclude that the automobile preference depends on the gender of the buyer?
Your test must include H0/HA, a decision with justification and a conclusion.
2-Wheel Drive 4-Wheel Drive Total
Male 23 43 66
Female 18 6 24
Total 41 49 90
Pg 1 of 5
, OPMT 1197
Business Statistics
2. In a survey involving 200 cars, each vehicle was classified according to whether or not it had
antilock brakes and whether or not it had been involved in an accident in the past year.
Antilock Brakes?
Accident? Yes No Total
Yes 9 11 20
No 141 39 180
Total 150 50 200
(a) What percentage of cars had been involved in an accident in the past year?
(b) What percentage of cars with antilock brakes had been in an accident in the past year?
(c) What percentage of cars without antilock brakes had been in an accident in the past year?
(d) Based on your answers above, do antilock brakes seem to help reduce the accident rate?
(does whether or not a car is in an accident depend on whether it had antilock brakes?)
(e) Does the data provide sufficient evidence that the accident rate for cars with antilock
differs from those without antilock brakes? Test at the 1% level of significance.
3. The Provincial government is considering implementing a new anti-smoking law which
would ban smoking in apartments and hotel rooms. They want to see if men hold the same
opinion on the proposed smoking ban as women. 500 randomly selected British Columbians
are cross-classified by their sex and opinion on the smoking ban. The results are below:
Opinion of the Smoking Ban
Gender Against Neutral In Favour Total
Male 71 36 133 240
Female 54 39 167 260
Total 125 75 300 500
(a) Is there enough evidence to conclude that men's opinions on the smoking ban differ
significantly from women's opinions? Test at the 5% level of significance. Your test
must include H0/HA, a decision with justification and a conclusion.
(b) Estimate the P-value
4. You own a store that sells household appliances. You make a very good margin selling
extended warranties on appliances. You want to investigate who buys these and so you take
a sample of 110 customers. You estimate their ages and obtain the following data about who
buys or doesn't buy the extended warranty.
Under 30 30 to 50 Over 50 Total
Buy 15 33 18 66
Did Not Buy 18 22 4 44
Total 33 55 22 110
You wish to see if customers of different ages respond differently when you offer to sell
them an extended warranty. Test the hypothesis at the 5% level of significance. Your test
must include H0/HA, a decision with justification and a conclusion.
Pg 2 of 5
