Question 1

Find the test statistic $\chi ^ { 2 }$ by McNemar's test.
-categorical data: a =25, b = 15, c = 20, d = 10
A) 5.600
B) 2.314
C) 0.457
D) 1.029

Accepted Answer

The answer of Find the test statistic \(\chi ^ {...

Question 2

Find the test statistic $\chi ^ { 2 }$ by McNemar's test.
-categorical data: a =72, b = 68, c = 110, d = 50
A) 7.934
B) 10.388
C) 9.444
D) 3.615

Accepted Answer

The McNemar's test statistic is calculated using the formula $\chi^2 = \frac{(b-c)^2}{b+c}$. Substituting the given values: $\chi^2 = \frac{(68-110)^2}{68+110} = \frac{1764}{178} = 9.444$.

Question 3

The table below summarizes results from an experiment in which subjects were classified as asthmatic or nonasthmatic and then given a treatment. After the treatment, they were again classified as asthmatic or nonasthmatic. Identify the
Discordant pairs of results.

A) The discordant pairs of results are (1) the 13 subjects who were asthmatic before the treatment and nonasthmatic after the treatment, and (2) the 12 subjects who were nonasthmatic before the treatment and nonasthmatic after the treatment.
B) The discordant pairs of results are (1) the 13 subjects who were nonasthmatic before the treatment and asthmatic after the treatment and (2) the 2 subjects who were asthmatic before the treatment and nonasthmatic after the treatment.
C) The discordant pairs of results are (1) the 2 subjects who were nonasthmatic before the treatment and asthmatic after the treatment, and (2) the 7 subjects who were asthmatic before the treatment and asthmatic after the treatment.
D) The discordant pairs of results are (1) the 2 subjects who were nonasthmatic before the treatment and asthmatic after the treatment, and (2) the 13 subjects who were asthmatic before the treatment and nonasthmatic after the treatment.

Accepted Answer

Discordant pairs are those where the subjects change from being asthmatic to nonasthmatic or nonasthmatic to asthmatic after the treatment. So, the first discordant pair is (2) the 2 subjects who were nonasthmatic before the treatment and asthmatic after the treatment, and the second discordant pair is (1) the 13 subjects who were asthmatic before the treatment and nonasthmatic after the treatment, making choice D the correct answer.

Question 4

The table below summarizes results from an experiment in which subjects were classified as diabetic or nondiabetic and then given a treatment. After the treatment, they were again classified as diabetic or
Nondiabetic. Which combinations of before treatment/after treatment categories will yield discordant pairs?

A) Only nondiabetic/nondiabetic
B) diabetic/nondiabetic and nondiabetic/diabetic
C) nondiabetic/nondiabetic and diabetic/diabetic
D) Only diabetic/nondiabetic

Accepted Answer

Discordant pairs occur when the before and after treatment categories do not match. Therefore, the combinations of diabetic/nondiabetic and nondiabetic/diabetic will yield discordant pairs. The other combinations (only nondiabetic/nondiabetic and only diabetic/nondiabetic) will not yield discordant pairs because the classifications remain the same before and after the treatment.

Question 5

The table below summarizes results from an experiment in which subjects were classified as asthmatic or nonasthmatic and then given a treatment. After the treatment, they were again classified as asthmatic or nonasthmatic. How many
Subjects changed their asthmatic/nonasthmatic status after the experiment?

A) 16
B) 32
C) 15
D) 17

Accepted Answer

The answer of The table below summarizes results from an...

Question 6

Use the sample data below to test whether car color affects the likelihood of being in an accident. Use a
significance level of 0.01. $$\begin{array} { r | r r r } 
& \text { Red } & \text { Blue } & \text { White } \
\hline \text { Car has been in } & & & \
\text { accident } & 28 & 33 & 36 \
\text { Car has not been } & & & \
\text { in accident } & 23 & 22 & 30
\end{array}$$

Accepted Answer

The answer of Use the sample data below to test...

Question 7

The table below summarizes results from an experiment in which subjects were classified as asthmatic or nonasthmatic and then given a treatment. After the treatment, they were again classified as asthmatic or nonasthmatic. Using a 0.05 Significance level, find the critical value.

A) $5.024$
B) $6.635$
C) $7.879$
D) $3.841$

Accepted Answer

The critical value for this experiment is found using the chi-square distribution with one degree of freedom (df = 1), since there are two categories (asthmatic and nonasthmatic) and one treatment. Looking at a chi-square distribution table with df = 1 and a significance level of 0.05, we find the critical value to be approximately 3.841. Therefore, the answer is choice D).

Question 8

At a high school debate tournament, half of the teams were asked to wear suits and ties and the rest were asked
to wear jeans and t-shirts. The results are given in the table below. Test the hypothesis at the 0.05 level that the
proportion of wins is the same for teams wearing suits as for teams wearing jeans. $$\begin{array} { r | r r } 
& \text { Win } & \text { Loss } \
\hline \text { Suit } & 22 & 28 \
\text { T-shirt } & 28 & 22
\end{array}$$

Accepted Answer

The answer of At a high school debate tournament, half...

Question 9

The table below summarizes results from an experiment in which subjects were classified as asthmatic or nonasthmatic and then given a treatment. After the treatment, they were again classified as asthmatic or nonasthmatic. How many
Subjects appeared to be unaffected by the treatment one way or the other?

A) 17
B) 32
C) 15
D) 8

Accepted Answer

To determine the number of subjects unaffected by the treatment, we need to look at the diagonal cells of the table, which represent the number of subjects who stayed in the same classification (asthmatic or nonasthmatic) before and after the treatment. In this case, there are 15 subjects who stayed in the same classification, meaning they were unaffected by the treatment. Therefore, the answer is (C) 15.

Question 10

A researcher wishes to test whether the proportion of college students who smoke is the same in four different
colleges. She randomly selects 100 students from each college and records the number that smoke. The results
are shown below. $$\begin{array} { r | r r r r } 
& \text { College A } & \text { College B } & \text { College C } & \text { College D } \
\hline \text { Smoke } & 17 & 26 & 11 & 34 \
\text { Don't smoke } & 83 & 74 & 89 & 66
\end{array}$$ Use a 0.01 significance level to test the claim that the proportion of students smoking is the same at all four
colleges.

Accepted Answer

The answer of A researcher wishes to test whether the...

Question 11

The table below summarizes results from an experiment in which subjects were classified as asthmatic or
nonasthmatic and then given a treatment. After the treatment, they were again classified as asthmatic or
nonasthmatic. Explain why McNemar's test ignores the frequencies of 9 and 11.

Accepted Answer

The answer of The table below summarizes results from an...

Question 12

Find the test statistic $\chi ^ { 2 }$ by McNemar's test.
-categorical data: a =50, b = 60, c = 85, d = 15
A) 4.267
B) 3.972
C) 4.303
D) 5.673

Accepted Answer

McNemar's test statistic is calculated using the formula $\chi^2 = \frac{(b-c)^2}{b+c}$. Substituting the given values: $\chi^2 = \frac{(60-85)^2}{60+85} = \frac{625}{145} \approx 4.31$. However, the closest option is B) 3.972, which suggests a rounding or calculation error in the options provided.

Question 13

The table below summarizes results from an experiment in which subjects were classified as asthmatic or nonasthmatic and then given a treatment. After the treatment, they were again classified as asthmatic or nonasthmatic.Using the
Appropriate frequencies, find the value of the test statistic. Round to three decimal places if necessary.

A) $8.471$
B) $9.882$
C) $0.701$
D) $9.941$

Accepted Answer

The answer of The table below summarizes results from an...

Question 14

A survey conducted in a small town yielded the results shown in the table. $\begin{array}{l|lc} 
& \multicolumn{2}{|l}{\text { Men Women }} \
\hline \text { Plan to vote } & 105 & 87 \
\hline \text { Do not plan to vote } & 312 & 246
\end{array}$

i) Test the claim that the intention to vote in the next presidential election is independent of the gender of the person being surveyed. Use a $0.05$ significance level.
ii) Using Yates' correction, replace $\sum \frac { ( \mathrm { O } - \mathrm { E } ) ^ { 2 } } { \mathrm { E } }$ with $\sum \frac { ( | \mathrm { O } - \mathrm { E } | - 0.5 ) ^ { 2 } } { \mathrm { E } }$ and repeat the test. What effect does Yates' correction have on the value of the test statistic?

Accepted Answer

The answer of A survey conducted in a small town...

Question 15

A researcher wishes to test the effectiveness of a flu vaccination. 150 people are vaccinated, 180 people are
vaccinated with a placebo, and 100 people are not vaccinated. The number in each group who later caught the
flu was recorded. The results are shown below. $$\begin{array} { r | r r r } 
& \text { Vaccinated } & \text { Placebo } & \text { Control } \
\hline \text { Caught the flu } & 8 & 19 & 21 \
\text { Did not catch the flu } & 142 & 161 & 79
\end{array}$$ Use a 0.05 significance level to test the claim that the proportion of people catching the flu is the same in all
three groups.

Accepted Answer

The answer of A researcher wishes to test the effectiveness...

Question 16

Use a 0.01 significance level to test the claim that the proportion of men who plan to vote in the next election is
the same as the proportion of women who plan to vote. 300 men and 300 women were randomly selected and
asked whether they planned to vote in the next election. The results are shown below. $$\begin{array} { r | r r } 
& \text { Men } & \text { Women } \
\hline \text { Plan to vote } & 170 & 185 \
\text { Do not plan to vote } & 130 & 115
\end{array}$$

Accepted Answer

The answer of Use a 0.01 significance level to test...

Question 17

The table below summarizes results from an experiment in which subjects were classified as asthmatic or nonasthmatic and then given a treatment. After the treatment, they were again classified as asthmatic or nonasthmatic. Using the
Values of the test statistic and critical value for a 0.05 significance level, what do you conclude? 
A) Fail to reject the null hypothesis that the following proportions are equal: (1) The proportion of asthmatics who were nonasthmatic after the treatment; 1) the proportion of nonasthmatics who were asthmatic after
The treatment. The treatment does not appear to be effective.
B) Reject the null hypothesis that the following proportions are unequal: (1) The proportion of asthmatics who were nonasthmatic after the treatment; 1) the proportion of nonasthmatics who were asthmatic after
The treatment. The treatment appears to be effective.
C) Fail to reject the null hypothesis that the following proportions are unequal: (1) The proportion of asthmatics who were nonasthmatic after the treatment; 1) the proportion of nonasthmatics who were
Asthmatic after the treatment. The treatment does not appear to be effective.
D) Reject the null hypothesis that the following proportions are equal: (1) The proportion of asthmatics who were nonasthmatic after the treatment; 1) the proportion of nonasthmatics who were asthmatic after the
Treatment. The treatment appears to be effective.

Accepted Answer

The question is asking us to determine whether or not the treatment is effective. To do this, we need to compare the proportions of asthmatics who were nonasthmatic after treatment and the proportions of nonasthmatics who were asthmatic after treatment. The null hypothesis is that the proportions are equal, while the alternative hypothesis is that they are not equal. Since the question does not provide the actual proportions, we cannot perform a hypothesis test. However, it does provide us with the test statistic and critical value for a 0.05 significance level, allowing us to make a decision based on whether or not the test statistic falls within the rejection region. Looking at the choices, we see that only choice D rejects the null hypothesis, meaning that the proportions are not equal, and concludes that the treatment appears to be effective. Therefore, D is the best choice.

Question 18

The table below summarizes results from an experiment in which subjects were classified as asthmatic or nonasthmatic and then given a treatment. After the treatment, they were again classified as asthmatic or nonasthmatic. How many
Subjects were included in the experiment?  
A) 32
B) 15
C) 8
D) 24

Accepted Answer

The answer of The table below summarizes results from an...

Question 19

A survey conducted in a small business yielded the results shown in the table.

i) Test the claim that health care coverage is independent of gender. Use a $0.05$ significance level.
ii) Using Yates' correction, replace $\sum \frac { ( \mathrm { O } - \mathrm { E } ) ^ { 2 } } { \mathrm { E } }$ with $\sum \frac { ( | \mathrm { O } - \mathrm { E } | - 0.5 ) ^ { 2 } } { \mathrm { E } }$ and repeat the test. What effect does Yates' correction have on the value of the test statistic?

Accepted Answer

The answer of A survey conducted in a small business...

Question 20

A survey conducted in a small business yielded the results shown in the table.

i) Test the claim that health care coverage is independent of gender. Use a $0.05$ significance level.
ii) Using Yates' correction, replace $\sum \frac { ( \mathrm { O } - \mathrm { E } ) ^ { 2 } } { \mathrm { E } }$ with $\sum \frac { ( | \mathrm { O } - \mathrm { E } | - 0.5 ) ^ { 2 } } { \mathrm { E } }$ and repeat the test. What effect does Yates' correction have on the value of the test statistic?

Accepted Answer

The answer of A survey conducted in a small business...

Quiz 11: Goodness-Of-Fit and Contingency Tables

Find the test statistic χ2\chi ^ { 2 }χ2 by McNemar's test. -categorical data: a =25, b = 15, c = 20, d = 10

Find the test statistic χ2\chi ^ { 2 }χ2 by McNemar's test. -categorical data: a =72, b = 68, c = 110, d = 50

The table below summarizes results from an experiment in which subjects were classified as asthmatic or nonasthmatic and then given a treatment. After the treatment, they were again classified as asthmatic or nonasthmatic. Identify the Discordant pairs of results.

The table below summarizes results from an experiment in which subjects were classified as asthmatic or nonasthmatic and then given a treatment. After the treatment, they were again classified as asthmatic or nonasthmatic. Using a 0.05 Significance level, find the critical value.

The table below summarizes results from an experiment in which subjects were classified as asthmatic or nonasthmatic and then given a treatment. After the treatment, they were again classified as asthmatic or nonasthmatic. Explain why McNemar's test ignores the frequencies of 9 and 11.

Find the test statistic χ2\chi ^ { 2 }χ2 by McNemar's test. -categorical data: a =50, b = 60, c = 85, d = 15

The table below summarizes results from an experiment in which subjects were classified as asthmatic or nonasthmatic and then given a treatment. After the treatment, they were again classified as asthmatic or nonasthmatic. How many Subjects were included in the experiment?

Find the test statistic $\chi ^ { 2 }$ by McNemar's test. -categorical data: a =25, b = 15, c = 20, d = 10

Find the test statistic $\chi ^ { 2 }$ by McNemar's test. -categorical data: a =72, b = 68, c = 110, d = 50

Find the test statistic $\chi ^ { 2 }$ by McNemar's test. -categorical data: a =50, b = 60, c = 85, d = 15