Question 1

A researcher wishes to test whether the proportion of college students who smoke is the_
same at 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 2

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. $$\begin{array} { r | l l l } 
& \text { Live with Parent } & \text { Rent Apartment } & \text { Own Home } \
\hline \text { Male } & 20 & 26 & 19 \
\text { Female } & 18 & 28 & 26
\end{array}$$

Accepted Answer

A) Reject the null hypothesis. There is sufficient evident to warrant rejection of the claim that living accommodation and gender are independent. 
B) Reject the null hypothesis. There is not sufficient evident to warrant rejection of the claim that living accommodation and gender are independent. 
C) Fail to reject the null hypothesis. There is sufficient evident to warrant rejection of the claim that living accommodation and gender are independent. 
D) Fail to reject the null hypothesis. There is not sufficient evident to warrant rejection of the claim that living accommodation and gender are independent.

Question 3

Select the null hypothesis for a test of independence.

Accepted Answer

A) The row and column variables are independent. 
B) The row and column variables are dependent. 
C) The row and column variables are normally distributed. 
D) The row and column variables have equal means.

Question 4

Use a $X^2$
 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. $$\begin{array} { c | c c c } 
& \text { Rock } & \text { Pop } & \text { Classical } \
\hline \mathbf { 1 5 - 2 5 } & 50 & 85 & 73 \
\mathbf { 2 5 - 3 5 } & 68 & 91 & 60 \
\mathbf { 3 5 - 4 5 } & 90 & 74 & 77
\end{array}$$ Use a 5 percent level of significance to test the null hypothesis that age and preferred
music type are independent.

Accepted Answer

The answer of Use a $X^2$
 test to test the...

Question 5

Discuss the three characteristics of a chi-square distribution.

Accepted Answer

The answer of Discuss the three characteristics of a chi-square...

Question 6

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 7

Use a $X^2$
 test to test the claim that in the given contingency table, the row variable and the
column variable are independent. Tests for adverse reactions to a new drug yielded the results
given in the table. At the 0.05 significance level, test the claim that the treatment (drug or
placebo)is independent of the reaction (whether or not headaches were experienced). $$\begin{array} { r | c c } 
& \text { Drug } & \text { Placebo } \
\hline \text { Headaches } & 11 & 7 \
\text { No headaches } & 73 & 91
\end{array}$$

Accepted Answer

The answer of Use a $X^2$
 test to test the...

Question 8

The following table shows the number of employees who called in sick at a business for_
different days of a particular week. $$\begin{array} { r | c c c c c c c } 
\text { Day } & \text { Sun } & \text { Mon } & \text { Tues } & \text { Wed } & \text { Thurs } & \text { Fri } & \text { Sat } \
\hline \text { Number sick } & 8 & 12 & 7 & 11 & 9 & 11 & 12
\end{array}$$ i)At the 0.05 level of significance, test the claim that sick days occur with equal frequency on
the different days of the week.
ii)Test the claim after changing the frequency for Saturday to 152. Describe the effect of this
outlier on the test.

Accepted Answer

The answer of The following table shows the number of...

Question 9

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 10

Which statement is not true for goodness-of -fit tests?

Accepted Answer

A) Observed frequencies must be whole numbers. 
B) Expected frequencies must be whole numbers. 
C) The expected frequency is found assuming that the distribution is as claimed. 
D) The observed frequency is found from sample data values.

Question 11

Define categorical data and give an example.

Accepted Answer

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

Question 12

Discuss the three characteristics of a chi-square distribution._

Accepted Answer

The answer of Discuss the three characteristics of a chi-square...

Question 13

Describe a goodness-of-fit test. What assumptions are made when using a goodness-of-fit test?_

Accepted Answer

The answer of Describe a goodness-of-fit test. What assumptions are...

Question 14

True or False: For a test of independence, the population that the data has come from must be
normally distributed.

Accepted Answer

A) True 
 B)False

Question 15

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 16

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

Question 17

A survey conducted in a small business yielded the results shown in the table. $\begin{array} { l c c } & \text { Men } & \text { Women } \ \text { Health insurance } & 50 & 20 \ \text { No health insurance } & 30 & 10 \end{array}$
Test the claim that health care coverage is independent of gender. Use a $0.05$ significance level. What is the value of the test statistic?

Accepted Answer

A)  $\chi ^ { 2 } = 0.1637$ 
B)  $\chi ^ { 2 } = 3.841$ 
C)  $\chi ^ { 2 } = 8.263$ 
D)  $\chi ^ { 2 } = 5.821$

Question 18

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. $$\begin{array} { r | c c c c c } 
\text { Response } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \
\hline \text { Frequency } & 12 & 15 & 16 & 18 & 19
\end{array}$$

Accepted Answer

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

Question 19

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 20

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 χ2 value, large P-value 
B) Small χ2 value, small P-value 
C) Large χ2 value, large P-value 
D) Large χ2 value, small P-value

Exam 11: Chi-Square and Analysis of Variance

Select the null hypothesis for a test of independence.

Discuss the three characteristics of a chi-square distribution.

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

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

Which statement is not true for goodness-of -fit tests?

Define categorical data and give an example.

Discuss the three characteristics of a chi-square distribution._

Describe a goodness-of-fit test. What assumptions are made when using a goodness-of-fit test?_

True or False: For a test of independence, the population that the data has come from must be normally distributed.

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

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