Question 1

The chi-square goodness of fit test will be valid if the average of the expected cell frequencies is ______________.

Accepted Answer

A) Greater than 0 
B) Less than 5 
C) Between 0 and 5 
D) At least 1 
E) At least 5 
A) Greater than 0 
B) Less than 5 
C) Between 0 and 5 
D) At least 1 
E) At least 5 E

Question 2

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed frequencies.

Accepted Answer

$$\begin{array} { l c } 
\text { Interval } & \text { Observed Frequencies } \
39.99 \text { and less } & 12 \
40 - 59.99 & 18 \
60 - 79.99 & 15 \
80 \text { and higher } & 5
\end{array}$$ 
It is desired to test whether these measurements came from a normal population.Calculate the expected frequency for the interval 40-59.99.
20.365
Feedback:z = (40 - 50.02)/18.7 = -.55
z = (59.99 - 50.02)/18.7 = .52
P(-.55 ≤ z ≤ .52)= .6985 - .2912 = .4073
e = .4073 × 50 = 20.365

Question 3

In the past,of all the students enrolled in "Basic Business Statistics," 10 percent earned A's,20 percent earned B's,30 percent earned C's,20 percent earned D's,and the rest either failed or withdrew from the course.Dr.Johnson is a new professor teaching "Basic Business Statistics" for the first time this semester.At the conclusion of the semester,in Dr.Johnson's class of 60 students,there were 10 A's,20 B's,20 C's,5 D's,and 5 W's or F's.Assume that Dr.Johnson's class constitutes a random sample.Dr.Johnson wants to know if there is sufficient evidence to conclude that the grade distribution of his class is different from the historical grade distribution.Calculate the chi-square statistic.

Accepted Answer

χ² = 16.4 Feedback: $$\begin{array} { l } e _ { A } = ( .1 ) ( 60 ) = 10 ; e _ { B } = ( .2 ) ( 60 ) = 12 \ e _ { C } = ( .3 ) ( 60 ) = 18 ; e _ { D } = ( .2 ) ( 60 ) = 12 \ e _ { F , W } = ( .2 ) ( 60 ) = 12 \ \chi ^ { 2 } = \frac { ( 10 - 6 ) ^ { 2 } } { 6 } + \frac { ( 20 - 12 ) ^ { 2 } } { 12 } + \frac { ( 20 - 18 ) ^ { 2 } } { 18 } + \frac { ( 5 - 12 ) ^ { 2 } } { 12 } + \frac { ( 5 - 12 ) ^ { 2 } } { 12 } = 16.4 \end{array}$$

Question 4

The AAA Co.is interested in their employees' level of satisfaction in the benefit package that they offer compared to their major competitors.A consultant hired to conduct the satisfaction survey told AAA Co.that the distribution of level of satisfaction at other companies is displayed below:

Accepted Answer

\[\begin{array} { | l | r | } 
\hline \t

Question 5

When we carry out a chi-square test of independence,as the differences between the respective observed and expected frequencies decrease,the probability of concluding that the row variable is independent of the column variable:

Accepted Answer

A) Decreases. 
B) Increases. 
C) May decrease or increase depending on the number of rows and columns. 
D) Will be unaffecteD. 
A) Decreases. 
B) Increases. 
C) May decrease or increase depending on the number of rows and columns. 
D) Will be unaffecteD.

Question 6

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed frequencies.

Accepted Answer

\[\begin{array} { l c } 
\text { Interva

Question 7

In the past,of all the students enrolled in "Basic Business Statistics," 10 percent earned A's,20 percent earned B's,30 percent earned C's,20 percent earned D's,and the rest either failed or withdrew from the course.Dr.Johnson is a new professor teaching "Basic Business Statistics" for the first time this semester.At the conclusion of the semester,in Dr.Johnson's class of 60 students,there were 10 A's,20 B's,20 C's,5 D's,and 5 W's or F's.Assume that Dr.Johnson's class constitutes a random sample.Dr.Johnson wants to know if there is sufficient evidence to conclude that the grade distribution of his class is different from the historical grade distribution.Calculate the chi-square statistic.

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Question 3

Correct Answer:

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χ² = 16.4
Feedback: $\begin{array} { l } e _ { A } = ( .1 ) ( 60 ) = 10 ; e _ { B } = ( .2 ) ( 60 ) = 12 \\e _ { C } = ( .3 ) ( 60 ) = 18 ; e _ { D } = ( .2 ) ( 60 ) = 12 \\e _ { F , W } = ( .2 ) ( 60 ) = 12 \\\chi ^ { 2 } = \frac { ( 10 - 6 ) ^ { 2 } } { 6 } + \frac { ( 20 - 12 ) ^ { 2 } } { 12 } + \frac { ( 20 - 18 ) ^ { 2 } } { 18 } + \frac { ( 5 - 12 ) ^ { 2 } } { 12 } + \frac { ( 5 - 12 ) ^ { 2 } } { 12 } = 16.4\end{array}$

Accepted Answer

df = 4;χ²._05,4 = 9.49 Fee

Question 8

The following frequency table summarizes the ages of 60 shoppers at the local grocery store.

Accepted Answer

\[\begin{array} { | l | r | } 
\hline \t

Question 9

When we carry out a chi-square test of independence,the chi-square statistic is based on (rc - 1)degrees of freedom,where r and c denote,respectively,the number of rows and columns in the contingency table.

Accepted Answer

A) True 
 B)False

Question 10

A fastener manufacturing company uses a chi-square goodness of fit test to determine if a population of all lengths of ¼-inch bolts it manufactures is distributed according to a normal distribution.If we reject the null hypothesis,it is reasonable to assume that the population distribution is at least approximately normally distributed.

Accepted Answer

A) True 
 B)False

Question 11

In a contingency table,if all of the expected frequencies equal the observed frequencies,then we can conclude that there is a perfect association between rows and columns.

Accepted Answer

A) True 
 B)False

Question 12

The χ2 statistic is used to test whether the assumption of normality is reasonable for a given population distribution.The sample consists of 5000 observations and is divided into 6 categories (intervals).The degrees of freedom for the chi-square statistic are:

Accepted Answer

A) 4999 
B) 6 
C) 5 
D) 4 
E) 3 
A) 4999 
B) 6 
C) 5 
D) 4 
E) 3

Question 13

The distance traveled by buses before their first major motor failure is distributed below,with an estimated mean and standard deviation of 95.7 and 38.1.Also shown are the expected frequencies of these intervals if the original population was a normal distribution.

Accepted Answer

\[\begin{array} { | l | r | r | } 
\hlin

Question 14

A human resource manager is interested in whether absences occur during the week with equal frequency.The manager took a random sample of 100 absences and created the following table:

Accepted Answer

\[\begin{array} { | l | l | } 
\hline \t

Question 15

A U.S.-based Internet company offers an online proficiency course in basic accounting.Completing this online course satisfies the "Fundamentals of Accounting" course requirement in many MBA programs.In the first semester,315 students have enrolled in the course.The marketing research manager divided the country into seven regions of approximately equal population.The course enrollment values for each of the seven regions are given below.The management wants to know if there is equal interest in the course across all regions.

Accepted Answer

\[\begin{array} { c c } 
\text { Region

Question 16

The HR manager of a major office supply chain is interested in determining whether an employee's educational level has an effect on knowledge of their job.An exam was given to 120 employees.The results are below:

Accepted Answer

\[\begin{array} { | l | r | r | r | r |

Question 17

A special version of the chi-square goodness of fit test that involves testing the null hypothesis that all of the multinomial probabilities are equal is called the test for ___________.

Accepted Answer

A) goodness of fit 
B) statistical independence 
C) normality 
D) homogeneity 
A) goodness of fit 
B) statistical independence 
C) normality 
D) homogeneity

Question 18

A manufacturing company produces part A732 for the aerospace industry.This particular part can be manufactured using 3 different production processes.The management wants to know if the quality of the units of part A732 is the same for all three processes.The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items,Process 2 produced 12 defective units in 180 items,and Process 3 manufactured 9 defective units in 150 items.
Chi-Square Contingency Table Test for Independence \(\begin{array}{c}
\begin{array}{lll}
\text {  } \
\text { Row 1 } \ 
\text {  } \
\text {  } \
\text {  Row 2} \
\text {  } \
\text {  } \
\text { Total } \
\text {  } \
\text {  } \
\end{array}
\begin{array}{l}
\text {  } \
\hline \text { Observed } \
\hline \text { Expected } \
\hline(\mathrm{O}-\mathrm{E})^{2} / \mathrm{E} \
\hline \text { Observed } \
\hline \text { Expected } \
\hline(\mathrm{O}-\mathrm{E})^{2} / \mathrm{E} \
\hline \text { Observed } \
\hline \text { Expected } \
\hline(\mathrm{O}-\mathrm{E})^{2} / \mathrm{E}
\end{array}
\begin{array}{|l|}
\text { Col } 1\
\hline 29 \
\hline 21.05 \
\hline 3.00 \
\hline 211 \
\hline 218.95 \
\hline 0.29 \
\hline 240 \
\hline 240.00 \
\hline 3.29 \
\end{array}
\begin{array}{l}
\text { Col } 2\
\hline 12 \
\hline 15.79 \
\hline 0.91 \
\hline 168 \
\hline 164.21 \
\hline 0.09 \
\hline 180 \
\hline 180.00 \
\hline 1.00 \ 
\end{array}
\begin{array}{|l|}
\operatorname{Col} 3\
\hline 9 \
\hline 13.16 \
\hline 1.31 \
\hline 141 \
\hline 136.84 \
\hline 0.13 \
\hline 150 \
\hline 150.00 \
\hline 1.44 \ 
\end{array}
\begin{array}{r}
\text { Total } \
\hline 50 \
\hline 50.00 \
\hline 5.22 \
\hline 520 \
\hline 520.00 \
\hline 0.50 \
\hline 570 \
\hline 570.00 \
\hline 5.73 
\end{array}
\end{array}\)

$\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\begin{array}{cc}
5.73 & \text { chi-square } \
.0571 & \text { p-value }
\end{array}$

At a significance level of .10,the management wants to perform a hypothesis test to determine if the quality of the items produced appears to be independent of the production process used.Based on the results summarized in the MegaStat/Excel output provided in the table above,we:

Accepted Answer

A) Reject H0 and conclude that the quality of the product is not the same for all processes. 
B) Reject H0 and conclude that the quality of the product is dependent on the manufacturing process. 
C) Do not reject H0,and conclude that the quality of the product does not significantly differ among the three processes. 
D) Reject H0 and conclude that the quality of the product is independent of the production process utilizeD. 
E) Both Reject H0 and conclude that the quality of the product is not the same for all processes and Reject H0 and conclude that the quality of the product is dependent on the manufacturing process are correct. 
A) Reject H0 and conclude that the quality of the product is not the same for all processes. 
B) Reject H0 and conclude that the quality of the product is dependent on the manufacturing process. 
C) Do not reject H0,and conclude that the quality of the product does not significantly differ among the three processes. 
D) Reject H0 and conclude that the quality of the product is independent of the production process utilizeD. 
E) Both Reject H0 and conclude that the quality of the product is not the same for all processes and Reject H0 and conclude that the quality of the product is dependent on the manufacturing process are correct.

Question 19

The chi-square goodness of fit test for multinomial probabilities with 5 categories has _____ degrees of freedom.

Accepted Answer

A) 5 
B) 4 
C) 3 
D) 6 
A) 5 
B) 4 
C) 3 
D) 6

Question 20

The following frequency table summarizes the ages of 60 shoppers at the local grocery store.

Accepted Answer

\[\begin{array} { | l | r | } 
\hline \t

The chi-square goodness of fit test will be valid if the average of the expected cell frequencies is ______________.

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed frequencies.

The AAA Co.is interested in their employees' level of satisfaction in the benefit package that they offer compared to their major competitors.A consultant hired to conduct the satisfaction survey told AAA Co.that the distribution of level of satisfaction at other companies is displayed below:

When we carry out a chi-square test of independence,as the differences between the respective observed and expected frequencies decrease,the probability of concluding that the row variable is independent of the column variable:

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed frequencies.

The following frequency table summarizes the ages of 60 shoppers at the local grocery store.

When we carry out a chi-square test of independence,the chi-square statistic is based on (rc - 1)degrees of freedom,where r and c denote,respectively,the number of rows and columns in the contingency table.

In a contingency table,if all of the expected frequencies equal the observed frequencies,then we can conclude that there is a perfect association between rows and columns.

The χ² statistic is used to test whether the assumption of normality is reasonable for a given population distribution.The sample consists of 5000 observations and is divided into 6 categories (intervals).The degrees of freedom for the chi-square statistic are:

The distance traveled by buses before their first major motor failure is distributed below,with an estimated mean and standard deviation of 95.7 and 38.1.Also shown are the expected frequencies of these intervals if the original population was a normal distribution.

A human resource manager is interested in whether absences occur during the week with equal frequency.The manager took a random sample of 100 absences and created the following table:

The HR manager of a major office supply chain is interested in determining whether an employee's educational level has an effect on knowledge of their job.An exam was given to 120 employees.The results are below:

A special version of the chi-square goodness of fit test that involves testing the null hypothesis that all of the multinomial probabilities are equal is called the test for ___________.

The chi-square goodness of fit test for multinomial probabilities with 5 categories has _____ degrees of freedom.

The following frequency table summarizes the ages of 60 shoppers at the local grocery store.

Statistical Inferences for Population Variances

Experimental Design and Analysis of Variance

Simple Linear Regression Analysis

Multiple Regression and Model Building

Time Series Forecasting and Index Numbers

Process Improvement Using Control Charts

Nonparametric Methods

Decision Theory

Filters

Exam 13: Chi-Square Tests

The chi-square goodness of fit test will be valid if the average of the expected cell frequencies is ______________.

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed frequencies.

The AAA Co.is interested in their employees' level of satisfaction in the benefit package that they offer compared to their major competitors.A consultant hired to conduct the satisfaction survey told AAA Co.that the distribution of level of satisfaction at other companies is displayed below:

When we carry out a chi-square test of independence,as the differences between the respective observed and expected frequencies decrease,the probability of concluding that the row variable is independent of the column variable:

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed frequencies.

The following frequency table summarizes the ages of 60 shoppers at the local grocery store.

When we carry out a chi-square test of independence,the chi-square statistic is based on (rc - 1)degrees of freedom,where r and c denote,respectively,the number of rows and columns in the contingency table.

In a contingency table,if all of the expected frequencies equal the observed frequencies,then we can conclude that there is a perfect association between rows and columns.

The χ2 statistic is used to test whether the assumption of normality is reasonable for a given population distribution.The sample consists of 5000 observations and is divided into 6 categories (intervals).The degrees of freedom for the chi-square statistic are:

The distance traveled by buses before their first major motor failure is distributed below,with an estimated mean and standard deviation of 95.7 and 38.1.Also shown are the expected frequencies of these intervals if the original population was a normal distribution.

A human resource manager is interested in whether absences occur during the week with equal frequency.The manager took a random sample of 100 absences and created the following table:

The HR manager of a major office supply chain is interested in determining whether an employee's educational level has an effect on knowledge of their job.An exam was given to 120 employees.The results are below:

A special version of the chi-square goodness of fit test that involves testing the null hypothesis that all of the multinomial probabilities are equal is called the test for ___________.

The chi-square goodness of fit test for multinomial probabilities with 5 categories has _____ degrees of freedom.

The following frequency table summarizes the ages of 60 shoppers at the local grocery store.

Statistical Inferences for Population Variances

Experimental Design and Analysis of Variance

Simple Linear Regression Analysis

Multiple Regression and Model Building

Time Series Forecasting and Index Numbers

Process Improvement Using Control Charts

Nonparametric Methods

Decision Theory

Filters

The χ² statistic is used to test whether the assumption of normality is reasonable for a given population distribution.The sample consists of 5000 observations and is divided into 6 categories (intervals).The degrees of freedom for the chi-square statistic are: