MATH 22N STATISTICS WEEK 4
Contingency tables
1. Researchers wanted to study if couples having children are married. They surveyed a
large group of people. The data are shown in the contingency table below. What is
the relative risk of having children for those who are married? Round your answer to
two decimal places.
Children no children total
Married – 97 35 132
Not married- 68 71 139
Total 165 106 271
1.50
The probability that someone who is married has children is 97/132. The probability
that someone who is not married has children is 68/139. The relative risk is
then 97/132 divided by 68/139≈1.50. This means that in this survey, people who are
married were 150% as likely to have children as people who are not married
2. A survey of 155 employed citizens was conducted and the results are shown in the
table below. Given that a randomly selected survey participant does not work in an
office, what is the probability that this person works on Saturday?
Enter your answer as a fraction.
Does not Work in an Office Works in an Office Total
Does not Work Saturday 32 62 94
Works Saturday 14 47 61
Total 46 109 155
7/23
The total number of those not working in an office is 46. Of these, 14 work on
Saturday. Therefore, the probability that a randomly selected person from those not
working in an office works on Saturday is 14/46=7/23
3. Researchers wanted to study if having a long beak is related to flight in birds. They
surveyed a total of 34 birds. The data are shown in the contingency table below.
What is the odds ratio for birds having long beaks being able to fly against birds not
having long beaks being able to fly? Round your answer to two decimal places.
Flies Does not fly Total
, Long beak 11 3 14
Not a long beak 7 13 20
Total 18 16 34
The odds that a bird that has a long beak also flies are 11 to 3. The odds that a bird
that does not have a long beak flies are 7 to 13. The odds ratio is then 11/3 divided
by 7/13≈6.81. In this study, birds that have long beaks had almost 7 times the odds
of also being able to fly as the birds that do not have long beaks.
4. Fill in the following contingency table and find the number of students who both
play sports AND play an instrument.
Students play instrument doesn’t play instrument total
Play sports
Doesn’t play sport 10
Total 67 99
By using the known totals along the rows and columns you can fill in the rest of the
contingency table. For example, looking at the row of totals in the table, we know
that the unknown number plus 67 is 99, so the missing number must be 32.
Continuing in this way, we can fill in the entire table:
From this, we can see that the number of students who both play sports and play an
instrument is 35.
5. Part-time Full-time Total
No Gym Membership 22 65 87
Gym Membership 7 61 68
Total 29 126 155
A group of 155 students at a private university were asked if they are full-time or
part-time and if they have gym memberships. The results are shown in the table
above. Given that a randomly selected survey participant is part-time, what is the
probability that this student has a gym membership?
7/29
6. Fill in the following contingency table and find the number of students who both
have a cat AND have a dog.
Contingency tables
1. Researchers wanted to study if couples having children are married. They surveyed a
large group of people. The data are shown in the contingency table below. What is
the relative risk of having children for those who are married? Round your answer to
two decimal places.
Children no children total
Married – 97 35 132
Not married- 68 71 139
Total 165 106 271
1.50
The probability that someone who is married has children is 97/132. The probability
that someone who is not married has children is 68/139. The relative risk is
then 97/132 divided by 68/139≈1.50. This means that in this survey, people who are
married were 150% as likely to have children as people who are not married
2. A survey of 155 employed citizens was conducted and the results are shown in the
table below. Given that a randomly selected survey participant does not work in an
office, what is the probability that this person works on Saturday?
Enter your answer as a fraction.
Does not Work in an Office Works in an Office Total
Does not Work Saturday 32 62 94
Works Saturday 14 47 61
Total 46 109 155
7/23
The total number of those not working in an office is 46. Of these, 14 work on
Saturday. Therefore, the probability that a randomly selected person from those not
working in an office works on Saturday is 14/46=7/23
3. Researchers wanted to study if having a long beak is related to flight in birds. They
surveyed a total of 34 birds. The data are shown in the contingency table below.
What is the odds ratio for birds having long beaks being able to fly against birds not
having long beaks being able to fly? Round your answer to two decimal places.
Flies Does not fly Total
, Long beak 11 3 14
Not a long beak 7 13 20
Total 18 16 34
The odds that a bird that has a long beak also flies are 11 to 3. The odds that a bird
that does not have a long beak flies are 7 to 13. The odds ratio is then 11/3 divided
by 7/13≈6.81. In this study, birds that have long beaks had almost 7 times the odds
of also being able to fly as the birds that do not have long beaks.
4. Fill in the following contingency table and find the number of students who both
play sports AND play an instrument.
Students play instrument doesn’t play instrument total
Play sports
Doesn’t play sport 10
Total 67 99
By using the known totals along the rows and columns you can fill in the rest of the
contingency table. For example, looking at the row of totals in the table, we know
that the unknown number plus 67 is 99, so the missing number must be 32.
Continuing in this way, we can fill in the entire table:
From this, we can see that the number of students who both play sports and play an
instrument is 35.
5. Part-time Full-time Total
No Gym Membership 22 65 87
Gym Membership 7 61 68
Total 29 126 155
A group of 155 students at a private university were asked if they are full-time or
part-time and if they have gym memberships. The results are shown in the table
above. Given that a randomly selected survey participant is part-time, what is the
probability that this student has a gym membership?
7/29
6. Fill in the following contingency table and find the number of students who both
have a cat AND have a dog.
