Question 1

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 2

While conducting a goodness-of-fit test if the observed and expected values are close, you would expect which of the following:

Accepted Answer

A)  Small $\chi ^ { 2 }$ value, large $P$-value 
B)  Large $\chi ^ { 2 }$ value, large $P$-value 
C)  Small $\chi ^ { 2 }$ value, small $P$-value 
D)  Large $\chi ^ { 2 }$ value, small $P$-value

Question 3

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 4

An observed frequency distribution is as follows: $\begin{array}{l|ccc}
\text { Number of successes } & 0 & 1 & 2 \
\hline \text { Frequency } & 47 & 98 & 55
\end{array}$

i) Assuming a binomial distribution with $n = 2$ and $p = 1 / 2$, use the binomial formula to find the probability corresponding to each category of the table.
ii) Using the probabilities found in part (i), find the expected frequency for each category.
iii) Use a $0.05$ level of significance to test the claim that the observed frequencies fit a binomial distribution for which $\mathrm { n } = 2$ and $\mathrm { p } = 1 / 2$.

Accepted Answer

The answer of An observed frequency distribution is as follows:...

Question 5

According to Benford's Law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. Test for goodness-of-fit with Benford's Law. $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Leading Digit } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \
\hline \begin{array} { c } 
\text { Benford's law: } \
\text { distribution of } \
\text { leading digits }
\end{array} & 30.1 \% & 17.6 \% & 12.5 \% & 9.7 \% & 7.9 \% & 6.7 \% & 5.8 \% & 5.1 \% & 4.6 \% \
\hline
\end{array}$$ When working for the Brooklyn District Attorney, investigator Robert Burton analyzed the leading digits of the Amounts from 784 checks issued by seven suspect companies. The frequencies were found to be 0, 12, 0, 73, 482, 186, 8, 23, and 0, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed Frequencies are substantially different from the frequencies expected with Benford's Law, the check amounts Appear to result from fraud. Use a 0.05 significance level to test for goodness-of-fit with Benford's Law. What is The value of the test statistic? Does it appear that the checks are the result of fraud?

Accepted Answer

A)  $\chi ^ { 2 } = 15.507$ It does not appear that the checks are the result of fraud. 
B)  $\chi ^ { 2 } = 3177.409$ It does appear that the checks are the result of fraud. 
C)  $\chi ^ { 2 } = 15.507$ It does appear that the checks are the result of fraud. 
D)  $\chi ^ { 2 } = 3177.409$ It does not appear that the checks are the result of fraud.

Question 6

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

Accepted Answer

A)  5.600 
B)  2.314 
C)  0.457 
D)  1.029

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. Identify the
Discordant pairs of results.

Accepted Answer

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.

Question 8

Use a $x ^ { 2 }$ test to test the claim that in the given contingency table, the row variable and the column variable are
independent. Responses to a survey question are broken down according to employment status and the sample
results are given below. At the 0.10 significance level, test the claim that response and employment status are
independent. $$\begin{array} { r | c c c } 
& \text { Yes } & \text { No } & \text { Undecided } \
\hline \text { Employed } & 30 & 15 & 5 \
\text { Unemployed } & 20 & 25 & 10
\end{array}$$

Accepted Answer

The answer of Use a $x ^ { 2 }$...

Question 9

Using the data below and a 0.05 significance level, test the claim that the responses occur with percentages of
15%, 20%, 25%, 25%, and 15% respectively. $$\begin{array} { r | c c c c c } 
\text { Response } & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } & \mathrm { E } \
\hline \text { Frequency } & 12 & 15 & 16 & 18 & 19
\end{array}$$

Accepted Answer

The answer of Using the data below and a 0.05...

Question 10

Responses to a survey question are broken down according to employment status and the sample results are
given below. At the 0.10 significance level, test the claim that response and employment status are independent. $$\begin{array} { r | r r r } 
& \text { Yes } & \text { No } & \text { Undecided } \
\hline \text { Employed } & 30 & 15 & 5 \
\text { Unemployed } & 20 & 25 & 10
\end{array}$$

Accepted Answer

The answer of Responses to a survey question are broken...

Question 11

Perform the indicated goodness-of-fit test. You roll a die 48 times with the following results. $$\begin{array} { l | c | c | c | c | c | c } 
\text { Number } & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \text { Frequency } & 4 & 13 & 2 & 14 & 13 & 2
\end{array}$$ Use a significance level of 0.05 to test the claim that the die is fair.

Accepted Answer

The answer of Perform the indicated goodness-of-fit test. You roll...

Question 12

Perform the indicated goodness-of-fit test. You roll a die 48 times with the following results. $$\begin{array} { c | r | r | r | r | r | r } 
\text { Number } & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \text { Frequency } & 4 & 13 & 2 & 14 & 13 & 2
\end{array}$$ Use a significance level of 0.05 to test the claim that the die is fair.

Accepted Answer

The answer of Perform the indicated goodness-of-fit test. You roll...

Question 13

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 14

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 claim at the 0.05 level that the
Proportion of wins is the same for teams wearing suits as for teams wearing jeans. $$\begin{array} { l | c c } 
& \text { Win } & \text { Loss } \
\hline \text { Suit } & 22 & 28 \
\text { T-Shirt } & 28 & 22
\end{array}$$ What is your conclusion about the null hypothesis?

Accepted Answer

A)  Fail to support the null hypothesis. 
B)  Fail to reject the null hypothesis. 
C)  Reject the null hypothesis. 
D)  Support the null hypothesis.

Question 15

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. In order to test the claim at the 0.05 level that
The proportion of wins is the same for teams wearing suits as for teams wearing jeans, what would the null
Hypothesis be? $$\begin{array} { l | c c } 
& \text { Win } & \text { Loss } \
\hline \text { Suit } & 22 & 28 \
\text { T-Shirt } & 28 & 22
\end{array}$$

Accepted Answer

A)  The mean number of wins is different for teams wearing suits as for teams wearing jeans. 
B)  The proportions of wins is the same for teams wearing suits as for teams wearing jeans. 
C)  The proportions of wins is different for teams wearing suits as for teams wearing jeans. 
D)  The mean number of wins is the same for teams wearing suits as for teams wearing jeans.

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

A table summarizes the success and failures when subjects used different methods (yoga, acupuncture, and
chiropractor) to relieve back pain. If we test the claim at a 5% level of significance that success is independent of
the method used, technology provides a P-value of 0.0655. What does the P-value tell us about the claim?

Accepted Answer

The answer of A table summarizes the success and failures...

Question 18

An observed frequency distribution of exam scores is as follows: $\begin{array}{l|ccccc}
\text { Exam Score } & \text { Under } 60 & 60-69 & 70-79 & 80-89 & 90-100 \
\hline \text { Frequency } & 30 & 30 & 140 & 60 & 40
\end{array}$
i) Assuming a normal distribution with $\mu = 75$ and $\sigma = 15$, find the probability of a randomly selected subject belonging to each class. (Use boundaries of $59.5,69.5,79.5,89.5,100$.)
ii) Using the probabilities found in part (i), find the expected frequency for each category.
iii) Use a $0.05$ significance level to test the claim that the exam scores were randomly selected from a normally distributed population with $\mu = 75$ and $\sigma = 15$.

Accepted Answer

The answer of An observed frequency distribution of exam scores...

Question 19

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 20

In studying the occurrence of genetic characteristics, the following sample data were obtained. You would like to test the claim that the characteristics occur with the same frequency at the 0.05 significance level. $$\begin{array} { l | c c c c c c } 
\text { Characteristic } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \
\hline \text { Frequency } & 28 & 30 & 45 & 48 & 39 & 39
\end{array}$$ What is the expected value for D?

Accepted Answer

A)  28 
B)  42 
C)  38 
D)  48

Exam 11: Goodness-Of-Fit and Contingency Tables

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.

While conducting a goodness-of-fit test if the observed and expected values are close, you would expect which of the following:

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

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.

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