Question 1

The table in number 18 is called a two-way table. Why is the terminology of two-way table used?

Accepted Answer

The answer of The table in number 18 is called...

Question 2

Perform the indicated goodness-of-fit test. Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market
researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in
Idaho, and 60 in Montana. At the 0.05 significance level, test the claim that the sample of 1000
subjects has a distribution that agrees with the distribution of state populations.

Accepted Answer

The answer of Perform the indicated goodness-of-fit test. Among the...

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.
$\begin{array} { r | r c c } 
& \text { Vaccinated } & \text { Placebo } & \text { Control } \
\hline \text { Caught the flu } & 8 & 19 & 21 \
\text { Did not catch the flu } & 142 & 161 & 79
\end{array}$

Accepted Answer

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

Question 4

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.
$\begin{array} { r | c c } 
& \text { Men } & \text { Women } \
\hline \text { Plan to vote } & 170 & 185 \
\text { Do not plan to vote } & 130 & 115
\end{array}$

Accepted Answer

The answer of Use a  0.01  significance level...

Question 5

Use a $\chi ^ { 2 }$ test to test the claim that in the given contingency table, the row variable and the column variable are independent. The table below shows the age and favorite type of music of 668 randomly selected people.
Use a 5 percent level of significance to test the null hypothesis that age and preferred music type are independent.
$\begin{array} { c | c c c } 
& \text { Rock } & \text { Pop } & \text { Classical } \
\hline \mathbf { 1 5 } - \mathbf { 2 5 } & 50 & 85 & 73 \
\mathbf { 2 5 - 3 5 } & 68 & 91 & 60 \
\mathbf { 3 5 } - 45 & 90 & 74 & 77
\end{array}$

Accepted Answer

The answer of Use a $\chi ^ { 2 }$...

Question 6

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 ...

Question 7

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | } 
\hline \text { Leading Digit } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \
\hline \begin{array} { l } 
\text { Benford's law: } \
\text { distribution of } \
\text { leading digits }
\end{array} & 30.1 \% & 17.6 \% & 12.5 \% & 9.7 \% & 7.9 \% & 6.7 \% & 5.8 \% & 5.1 \% & 4.6 \% \
\hline
\end{array}$$
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  0,18,0,79,476,180,8,23 , 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. Does it appear that the checks are the result of fraud?

Accepted Answer

The answer of According to Benford's Law, a variety of...

Question 8

Describe the null hypothesis for the test of independence. List the assumptions for the $\chi ^ { 2 }$test of independence.

Accepted Answer

The answer of Describe the null hypothesis for the test...

Question 9

Explain the computation of expected values for contingency tables in terms of probabilities. Refer to the assumptions of the null hypothesis as part of your explanation. You might give a
brief example to illustrate.

Accepted Answer

The answer of Explain the computation of expected values for...

Question 10

A survey of students at a college was asked if they lived at home with their parents, rented an apartment, or owned their own home. The results are shown in the table below sorted by gender. At $\alpha = 0.05$ test the claim that living accommodations are independent of the gender of the student.
$\begin{array} { r | c c c } 
& \text { Live with Parent } & \text { Rent Apartment } & \text { Own Home } \
\hline \text { Male } & 20 & 26 & 19 \
\text { Female } & 18 & 28 & 30
\end{array}$

Accepted Answer

The answer of A survey of students at a college...

Question 11

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.
$\begin{array} { r | c c c c } 
& \text { College A } & \text { College B } & \text { College C } & \text { College D } \
\hline \text { Smoke } & 17 & 26 & 11 & 34 \
\text { Don't Smoke } & 83 & 74 & 89 & 66
\end{array}$
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 12

Discuss the three characteristics of a chi-square distribution

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Question 13

In studying the responses to a multiple-choice test question, the following sample data were obtained. At the  0.05  significance level, test the claim that the responses occur with the same frequency.
$\begin{array} { r | c c c c c } 
\text { Response } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \
\hline \text { Frequency } & 12 & 15 & 16 & 18 & 19
\end{array}$

Accepted Answer

The answer of In studying the responses to a multiple-choice...

Question 14

Use a $\chi ^ { 2 }$ 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 $\chi ^ { 2 }$...

Question 15

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 16

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 17

Define categorical data and give an example

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The answer of Define categorical data and give an example...

Question 18

Describe a goodness-of-fit test.

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The answer of Describe a goodness-of-fit test....

Question 19

Describe the test of homogeneity. What characteristic distinguishes a test of homogeneity from a test of independence?

Accepted Answer

The answer of Describe the test of homogeneity. What characteristic...

Question 20

Use a $\chi ^ { 2 }$ test to test the claim that in the given contingency table, the row variable and the column variable are independent. 160 students who were majoring in either math or English were asked a test question, and the researcher recorded whether they answered the question correctly. The sample results are given below. At the  0.10  significance level, test the claim that response and major are independent.
$\begin{array} { r | c c } 
& \text { Correct } & \text { Incorrect } \
\hline \text { Math } & 27 & 53 \
\text { English } & 43 & 37
\end{array}$

Accepted Answer

The answer of Use a $\chi ^ { 2 }$...

Quiz 11: Goodness-Of-Fit and Contingency Tables

The table in number 18 is called a two-way table. Why is the terminology of two-way table used?

Describe the null hypothesis for the test of independence. List the assumptions for the $\chi ^ { 2 }$ test of independence.

Explain the computation of expected values for contingency tables in terms of probabilities. Refer to the assumptions of the null hypothesis as part of your explanation. You might give a brief example to illustrate.

Discuss the three characteristics of a chi-square distribution

Define categorical data and give an example

Describe a goodness-of-fit test.

Describe the test of homogeneity. What characteristic distinguishes a test of homogeneity from a test of independence?

Quiz 11: Goodness-Of-Fit and Contingency Tables

The table in number 18 is called a two-way table. Why is the terminology of two-way table used?

Describe the null hypothesis for the test of independence. List the assumptions for the χ2\chi ^ { 2 }χ2 test of independence.

Explain the computation of expected values for contingency tables in terms of probabilities. Refer to the assumptions of the null hypothesis as part of your explanation. You might give a brief example to illustrate.

Discuss the three characteristics of a chi-square distribution

Define categorical data and give an example

Describe a goodness-of-fit test.

Describe the test of homogeneity. What characteristic distinguishes a test of homogeneity from a test of independence?

Describe the null hypothesis for the test of independence. List the assumptions for the $\chi ^ { 2 }$ test of independence.