Deck 10: Multinomial Experiments and Contingency Tables

Question 1

Use the following sample data to answer the next questions. The table
represents results from an experiment with patients afflicted in both eyes with
glaucoma. Each patient was treated in one eye with laser surgery and in the other
eye was treated with eye drops. Using a .05 significance level, apply McNemar's
test to test the following claim: The proportion of patients with no improvement on
the laser treated eye and an improvement on the drops treated eye is the same as
the proportion of patients with an improvement on the laser treated eye and no
improvement on the drops treated eye.
State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Answer 1

Reject . It appears that the two treatments produce different results. Analyzing
the frequencies, the eye drop treatment appears to be more effective in treating
glaucoma.

Question 2

Use the following sample data to answer the next questions. Use a .05
significance level and the observed frequencies of 70 Neonatal deaths to test the
claim that number of neonatal deaths on each day of the week is equally likely.

What is the expected frequency for each of the seven categories?

Answer 2

E = 10

Question 3

Use the following sample data to answer the next questions. Using a .01
significance level, test the claim that the proportions of fear/do not fear responses are the same for male and female dental patients.
Identify the critical value.

Answer 3

critical value

Question 4

Use the following sample data to answer the next questions. The table
represents results from an experiment with patients afflicted in both eyes with
glaucoma. Each patient was treated in one eye with laser surgery and in the other
eye was treated with eye drops. Using a .05 significance level, apply McNemar's
test to test the following claim: The proportion of patients with no improvement on
the laser treated eye and an improvement on the drops treated eye is the same as
the proportion of patients with an improvement on the laser treated eye and no
improvement on the drops treated eye.
Identify the critical value.

Question 5

Use the following sample data to answer the next questions. Use a .05
significance level and the observed frequencies of 70 Neonatal deaths to test the
claim that number of neonatal deaths on each day of the week is equally likely.

State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Question 6

Use the following sample data to answer the next questions. Using a .01
significance level, test the claim that the proportions of fear/do not fear responses are the same for male and female dental patients.
Identify the null and alternative hypotheses.

Question 7

Use the following sample data to answer the next questions. Use a .05
significance level and the observed frequencies of 70 Neonatal deaths to test the
claim that number of neonatal deaths on each day of the week is equally likely.

Identify the null and alternative hypotheses.

Question 8

Use the following sample data to answer the next questions. Use a .05
significance level and the observed frequencies of 70 Neonatal deaths to test the
claim that number of neonatal deaths on each day of the week is equally likely.

Identify the critical value.

Question 9

Use the following sample data to answer the next questions. The table
represents results from an experiment with patients afflicted in both eyes with
glaucoma. Each patient was treated in one eye with laser surgery and in the other
eye was treated with eye drops. Using a .05 significance level, apply McNemar's
test to test the following claim: The proportion of patients with no improvement on
the laser treated eye and an improvement on the drops treated eye is the same as
the proportion of patients with an improvement on the laser treated eye and no
improvement on the drops treated eye.
Determine the value of the test statistic.

Question 10

Use the following sample data to answer the next questions. The table
represents results from an experiment with patients afflicted in both eyes with
glaucoma. Each patient was treated in one eye with laser surgery and in the other
eye was treated with eye drops. Using a .05 significance level, apply McNemar's
test to test the following claim: The proportion of patients with no improvement on
the laser treated eye and an improvement on the drops treated eye is the same as
the proportion of patients with an improvement on the laser treated eye and no
improvement on the drops treated eye.
Identify the null and alternative hypotheses.

Question 11

Use the following sample data to answer the next questions. Using a .01
significance level, test the claim that the proportions of fear/do not fear responses are the same for male and female dental patients.
Determine the value of the test statistic.

Question 12

For the next questions, identify the choice that contains a discordant pair.
Choose the following pair of results that are discordant.

A) Survived/Did not survive
B) Survived/Survived
C) Did not survive/Did not survive

Question 13

Use the following sample data to answer the next questions. Biologists
studying the re-forestation of two species of tropical trees in Brazil's Atlantic forest
examined the number of trees that survived based on whether they were planted at
a mine site or at a railroad embankment. Using a .05 significance level, test the
claim that whether a tree survives at a mine site or at a railroad embankment is
independent of the species of the tree.

State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Question 14

Use the following sample data to answer the next questions. Biologists
studying the re-forestation of two species of tropical trees in Brazil's Atlantic forest
examined the number of trees that survived based on whether they were planted at
a mine site or at a railroad embankment. Using a .05 significance level, test the
claim that whether a tree survives at a mine site or at a railroad embankment is
independent of the species of the tree.

Determine the value of the test statistic.

Question 15

For the next questions, identify the choice that contains a discordant pair.
Choose the following pair of results that are discordant.

A) Oppose/Oppose
B) Oppose/Favor
C) Favor/Favor

Question 16

Use the following sample data to answer the next questions. Using a .01
significance level, test the claim that the proportions of fear/do not fear responses are the same for male and female dental patients.
State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Question 17

Use the following sample data to answer the next questions. Biologists
studying the re-forestation of two species of tropical trees in Brazil's Atlantic forest
examined the number of trees that survived based on whether they were planted at
a mine site or at a railroad embankment. Using a .05 significance level, test the
claim that whether a tree survives at a mine site or at a railroad embankment is
independent of the species of the tree.

Identify the null and alternative hypotheses.

Question 18

Use the following sample data to answer the next questions. Biologists
studying the re-forestation of two species of tropical trees in Brazil's Atlantic forest
examined the number of trees that survived based on whether they were planted at
a mine site or at a railroad embankment. Using a .05 significance level, test the
claim that whether a tree survives at a mine site or at a railroad embankment is
independent of the species of the tree.

Identify the critical value.

Question 19

Use the following sample data to answer the next questions. The table
represents results from an experiment with patients afflicted in both eyes with
glaucoma. Each patient was treated in one eye with laser surgery and in the other
eye was treated with eye drops. Using a .05 significance level, apply McNemar's
test to test the following claim: The proportion of patients with no improvement on
the laser treated eye and an improvement on the drops treated eye is the same as
the proportion of patients with an improvement on the laser treated eye and no
improvement on the drops treated eye.
How many patients are included in the experiment?

Question 20

Use the following sample data to answer the next questions. Use a .05
significance level and the observed frequencies of 70 Neonatal deaths to test the
claim that number of neonatal deaths on each day of the week is equally likely.

Determine the value of the test statistic.

Question 21

Use the following sample data to answer the next questions. Using a .01
significance level, test the claim that the proportions of people who favor/oppose pro-choice on the abortion issue are the same for the males and females.

Determine the value of the test statistic.

Question 22

Use the following sample data to answer the next questions. The table
represents results from an experiment with patients afflicted with eczema on both
arms. Each patient was treated with an immune modulator cream on one arm and
a topical steroid cream on the other arm. Using a .05 significance level, apply
McNemar's test to test the following claim: The proportion of patients with no
cure on the immune modulator treated arm and a cure on the topical steroid
treated arm is the same as the proportion of patients with a cure on the immune
modulator treated arm and no cure on the topical steroid treated arm.

Determine the value of the test statistic.

Question 23

Use the following sample data to answer the next questions. Using a .01
significance level, test the claim that the proportions of people who favor/oppose pro-choice on the abortion issue are the same for the males and females.

State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Question 24

Use the following sample data to answer the next questions. The table
represents results from an experiment with patients afflicted with eczema on both
arms. Each patient was treated with an immune modulator cream on one arm and
a topical steroid cream on the other arm. Using a .05 significance level, apply
McNemar's test to test the following claim: The proportion of patients with no
cure on the immune modulator treated arm and a cure on the topical steroid
treated arm is the same as the proportion of patients with a cure on the immune
modulator treated arm and no cure on the topical steroid treated arm.

Identify the null and alternative hypotheses.

Question 25

Use the following sample data to answer the next questions. Use a .05
significance level and the observed frequencies of 144 drownings at the beaches of
a randomly selected coastal state to test the claim that the number of drownings for each month is equally likely.

Determine the value of the test statistic.

Question 26

Use the following sample data to answer the next questions. The table
represents results from an experiment with patients afflicted with eczema on both
arms. Each patient was treated with an immune modulator cream on one arm and
a topical steroid cream on the other arm. Using a .05 significance level, apply
McNemar's test to test the following claim: The proportion of patients with no
cure on the immune modulator treated arm and a cure on the topical steroid
treated arm is the same as the proportion of patients with a cure on the immune
modulator treated arm and no cure on the topical steroid treated arm.

Identify the critical value.

Question 27

Use the following sample data to answer the next questions. Use a .05
significance level and the observed frequencies of 144 drownings at the beaches of
a randomly selected coastal state to test the claim that the number of drownings for each month is equally likely.

Identify the null and alternative hypotheses.

Question 28

Use the following sample data to answer the next questions. The table
represents results from an experiment with patients afflicted with eczema on both
arms. Each patient was treated with an immune modulator cream on one arm and
a topical steroid cream on the other arm. Using a .05 significance level, apply
McNemar's test to test the following claim: The proportion of patients with no
cure on the immune modulator treated arm and a cure on the topical steroid
treated arm is the same as the proportion of patients with a cure on the immune
modulator treated arm and no cure on the topical steroid treated arm.

How many patients are included in the experiment?

Question 29

Use the following sample data to answer the next questions. Biologists
studying the re-introduction of two species of fish in the Pacific Ocean examined
fish survival after release based on two rearing strategies: rearing at a land-based
farm and rearing at an ocean-based farm. Using a .05 significance level, test the
claim that the survival of the species of fish is independent of rearing strategy.
Identify the null and alternative hypotheses.

Question 30

For the next questions, identify the choice that contains a discordant pair.
Choose the following pair of results that are discordant.

A) Survived/Survived
B) Did not survive/Did not survive
C) Survived/Did not survive

Question 31

Use the following sample data to answer the next questions. Biologists
studying the re-introduction of two species of fish in the Pacific Ocean examined
fish survival after release based on two rearing strategies: rearing at a land-based
farm and rearing at an ocean-based farm. Using a .05 significance level, test the
claim that the survival of the species of fish is independent of rearing strategy.
Identify the critical value.

Question 32

Use the following sample data to answer the next questions. Use a .05
significance level and the observed frequencies of 144 drownings at the beaches of
a randomly selected coastal state to test the claim that the number of drownings for each month is equally likely.

State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Question 33

Use the following sample data to answer the next questions. Biologists
studying the re-introduction of two species of fish in the Pacific Ocean examined
fish survival after release based on two rearing strategies: rearing at a land-based
farm and rearing at an ocean-based farm. Using a .05 significance level, test the
claim that the survival of the species of fish is independent of rearing strategy.
State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Question 34

Use the following sample data to answer the next questions. Using a .01
significance level, test the claim that the proportions of people who favor/oppose pro-choice on the abortion issue are the same for the males and females.

Identify the null and alternative hypotheses.

Question 35

Use the following sample data to answer the next questions. Use a .05
significance level and the observed frequencies of 144 drownings at the beaches of
a randomly selected coastal state to test the claim that the number of drownings for each month is equally likely.

Identify the critical value.

Question 36

Use the following sample data to answer the next questions. Using a .01
significance level, test the claim that the proportions of people who favor/oppose pro-choice on the abortion issue are the same for the males and females.

Identify the critical value.

Question 37

Use the following sample data to answer the next questions. Use a .05
significance level and the observed frequencies of 144 drownings at the beaches of
a randomly selected coastal state to test the claim that the number of drownings for each month is equally likely.

What is the expected frequency for each of the twelve categories?

Question 38

Use the following sample data to answer the next questions. Biologists
studying the re-introduction of two species of fish in the Pacific Ocean examined
fish survival after release based on two rearing strategies: rearing at a land-based
farm and rearing at an ocean-based farm. Using a .05 significance level, test the
claim that the survival of the species of fish is independent of rearing strategy.
Determine the value of the test statistic.

Question 39

Use the following sample data to answer the next questions. The table
represents results from an experiment with patients afflicted with eczema on both
arms. Each patient was treated with an immune modulator cream on one arm and
a topical steroid cream on the other arm. Using a .05 significance level, apply
McNemar's test to test the following claim: The proportion of patients with no
cure on the immune modulator treated arm and a cure on the topical steroid
treated arm is the same as the proportion of patients with a cure on the immune
modulator treated arm and no cure on the topical steroid treated arm.

State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Question 40

For the next questions, identify the choice that contains a discordant pair.
Choose the following pair of results that are discordant.

A) Fear/Fear
B) Fear/Do Not Fear
C) Do Not Fear/Do Not Fear 82