Question 1

Use a significance level of 0.05 and determine if the use of a cell phone and having an auto accident are independent.

Accepted Answer

Failed to reject Ho - they are independent
H_o:Using a cell phone and having an accident are independent
H_a:Using a cell phone and having an accident are dependent
χ² = 1.5023,χ²_.05,1 = 3.841
Reject H_o if χ² > χ²_.05,1 failed to reject Ho

Question 2

Consider a set of 50 measurements with a mean of 50.2 and a standard deviation of 18.7 and with the observed and expected frequencies reported below.It is desired to test whether these measurements came from a normal population.What is the value of the chi-square test statistic? $$\begin{array} { l c c } 
\text { Interval } & \text { Observed Frequencies } & \text { Expected frequencies } \
39.99 \text { and less } & 12 & 14.56 \
40 - 59.99 & 18 & 20.365 \
60 - 79.99 & 15 & 12.28 \
80 \text {-and higher } & 5 & 2.795
\end{array}$$

Accepted Answer

A) 2.82 
B) 3.07 
C) 6.79 
D) 8.28 
E) 10.56 
A) 2.82 
B) 3.07 
C) 6.79 
D) 8.28 
E) 10.56 B

Question 3

At a significance level of .05,test H0: the set of 50 measurements came from a normal population.

Accepted Answer

Fail to reject H₀,normal distribution

\begin{array} { l } \chi ^ { 2 } = \frac { ( 12 - 14.56 ) ^ { 2 } } { 14.56 } + \frac { ( 18 - 20.365 ) ^ { 2 } } { 20.365 } + \frac { ( 15 - 12.28 ) ^ { 2 } } { 12.28 } + \frac { ( 5 - 2.795 ) ^ { 2 } } { 2.795 } = 3.07 \\\chi _ { .05,1 } ^ { 2 } = 3.84\end{array}

3.07 < 3.84

, failed to reject

\mathrm { H } _ { 0 }

, normal distribution is appropriate.

Question 4

An internet company offers an on-line proficiency course in basic accounting.Completion of 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 populations.The course enrolment values in each of the seven regions are given below.The management wants to know if there is equal interest in the course across all regions. $$\begin{array} { c c } 
\text { Region } & \text { Enrolment } \
1 & 45 \
2 & 60 \
3 & 30 \
4 & 40 \
5 & 50 \
6 & 55 \
7 & 35
\end{array}$$
-Calculate the value of the chi-square statistic.

Accepted Answer

The answer of An internet company offers an on-line proficiency...

Question 5

Assume that H0: p1 = p2 = p3 = p4 = p5 = p6 = p7 is not rejected and state a one sentence managerial conclusion.

Accepted Answer

It appears that the enrolment

Question 6

On the most recent tax cut proposal,a random sample of men and women were asked how they would cast their votes.The results are presented below: $$\begin{array} { l c c c } 
& \text { Issue: Tax cut proposal } & \
& \text { Favour } & \text { Oppose } & \text { Abstain } \
\text { Men } & 85 & 78 & 37 \
\text { Women } & 118 & 61 & 25
\end{array}$$
-Calculate the chi-square statistic for this test of independence.

Accepted Answer

The answer of On the most recent tax cut proposal,a...

Question 7

Consider the 3 × 2 contingency table below.
$$\begin{array} { c c c } 
& { \text { Factor B } } \
\text { Factor A } & \mathrm { B } _ { 1 } & \mathrm {~B} _ { 2 } \
\mathrm {~A} _ { 1 } & 16 & 14 \
\mathrm {~A} _ { 2 } & 15 & 25 \
\mathrm {~A} _ { 3 } & 9 & 21
\end{array}$$
-Compute the expected frequencies in row 1.

Accepted Answer

The answer of Consider the 3 × 2 contingency table...

Question 8

Consider the 3 × 2 contingency table below.What is the expected value for A1B1? $$\begin{array} { c c c } 
&{ \text { Factor B } } \
\text { Factor A } & \mathrm { B } _ { 1 } & \mathrm {~B} _ { 2 } \
\mathrm {~A} _ { 1 } & 16 & 14 \
\mathrm {~A} _ { 2 } & 15 & 25 \
\mathrm {~A} _ { 3 } & 9 & 21
\end{array}$$

Accepted Answer

A) 12 
B) 14 
C) 16 
D) 18 
E) 20 
A) 12 
B) 14 
C) 16 
D) 18 
E) 20

Question 9

At a significance level of .05,test H0: the factors A and B are independent.

Accepted Answer

Fail to re

Question 10

A manufacturing company produces part 2205 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 2205 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.
-At a significance level of .05 we performed chi-square test of independence to determine if the quality of the items produced appear to be independent of the production process.What are the degrees of freedom for the chi-square statistic?

Accepted Answer

A) 2 
B) 3 
C) 520 
D) 569 
E) 570 
A) 2 
B) 3 
C) 520 
D) 569 
E) 570

Question 11

At a significance level of .05,test H0: the probabilities are equal for all seven regions.

Accepted Answer

Question 12

A manufacturing company produces part 2205 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 2205 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. At a significance level of .05, the management wants to perform a hypothesis test to determine whether the quality of items produced appears to be independent of the production process used.
-What is the rejection point condition?

Accepted Answer

A) Reject H0 if ?2 > .10257 
B) Reject H0 if ?2 > 9.3484 
C) Reject H0 if ?2 > 5.99147 
D) Reject H0 if ?2 > 7.37776 
E) Reject H0 if ?2 > 7.81473 
A) Reject H0 if ?2 > .10257 
B) Reject H0 if ?2 > 9.3484 
C) Reject H0 if ?2 > 5.99147 
D) Reject H0 if ?2 > 7.37776 
E) Reject H0 if ?2 > 7.81473

Question 13

A manufacturing company produces part 2205 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 2205 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. At a significance level of .05, the management wants to perform a hypothesis test to determine whether the quality of items produced appears to be independent of the production process used.
-Calculate the expected number of defective units produced by Process 1.

Accepted Answer

A) 29 
B) 21.053 
C) 218.947 
D) 6.042 
E) 10.786 
A) 29 
B) 21.053 
C) 218.947 
D) 6.042 
E) 10.786

Question 14

On the most recent tax cut proposal,a random sample of men and women were asked how they would cast their votes.The results are presented below: $$\begin{array} { l c c c } 
& \text { Issue: Tax cut proposal } & \
& \text { Favour } & \text { Oppose } & \text { Abstain } \
\text { Men } & 85 & 78 & 37 \
\text { Women } & 118 & 61 & 25
\end{array}$$
-Determine the expected frequencies for the chi-square test of independence.

Accepted Answer

100.5,68.8

Question 15

When we carry out a chi-square test of independence,if ri is row total for row i and cj is the column total for column j,then the estimated expected cell frequency corresponding to row i and column j equals (ri)(cj)/n.

Accepted Answer

A) True 
 B)False

Question 16

A manufacturing company produces part 2205 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 2205 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. At a significance level of .05, the management wants to perform a hypothesis test to determine whether the quality of items produced appears to be independent of the production process used.
-Calculate the expected number of conforming units produced by Process 2.

Accepted Answer

A) 15.789 
B) 168 
C) 180 
D) 164.211 
E) 83.076 
A) 15.789 
B) 168 
C) 180 
D) 164.211 
E) 83.076

Question 17

When we carry out a chi-square goodness of fit test for a normal distribution,the null hypothesis states that the population:

Accepted Answer

A) Does not have a normal distribution 
B) Has a normal distribution 
C) Has a chi-square distribution 
D) Does not have a chi-square distribution 
E) Has k-3 degrees of freedom 
A) Does not have a normal distribution 
B) Has a normal distribution 
C) Has a chi-square distribution 
D) Does not have a chi-square distribution 
E) Has k-3 degrees of freedom

Question 18

Consider the 3 × 2 contingency table below.What is the expected value for A3B1? $$\begin{array} { c c c } 
& { \text { Factor B } } \
\text { Factor A } & B _ { 1 } & B _ { 2 } \
\mathrm {~A} _ { 1 } & 16 & 14 \
\mathrm {~A} _ { 2 } & 15 & 25 \
\mathrm {~A} _ { 3 } & 9 & 21
\end{array}$$

Accepted Answer

A) 12 
B) 14 
C) 16 
D) 18 
E) 20 
A) 12 
B) 14 
C) 16 
D) 18 
E) 20

Question 19

How many degrees of freedom are associated with the chi-square test?

Accepted Answer

2
Degrees

Question 20

In the past, of all the students enrolled in "Basic Business Statistics", 10% earned A's 20% earned B's, 30% earned C's, 20% 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 this particular class is different than the historical grade distribution
-At ? = .05,test to determine if the grade distribution for Dr.Johnson's class is different than the historical grade distribution.

Accepted Answer

Reject H₀S1

Use a significance level of 0.05 and determine if the use of a cell phone and having an auto accident are independent.

At a significance level of .05,test H₀: the set of 50 measurements came from a normal population.

Assume that H₀: p₁ = p₂ = p₃ = p₄ = p₅ = p₆ = p₇ is not rejected and state a one sentence managerial conclusion.

On the most recent tax cut proposal,a random sample of men and women were asked how they would cast their votes.The results are presented below: Issue: Tax cut proposal Favour Oppose Abstain Men 85 78 37 Women 118 61 25 -Calculate the chi-square statistic for this test of independence.

Consider the 3 × 2 contingency table below. Factor B Factor A 16 14 15 25 9 21 -Compute the expected frequencies in row 1.

Consider the 3 × 2 contingency table below.What is the expected value for A₁B₁? Factor B Factor A 16 14 15 25 9 21

At a significance level of .05,test H₀: the factors A and B are independent.

At a significance level of .05,test H₀: the probabilities are equal for all seven regions.

On the most recent tax cut proposal,a random sample of men and women were asked how they would cast their votes.The results are presented below: Issue: Tax cut proposal Favour Oppose Abstain Men 85 78 37 Women 118 61 25 -Determine the expected frequencies for the chi-square test of independence.

When we carry out a chi-square test of independence,if r_i is row total for row i and c_j is the column total for column j,then the estimated expected cell frequency corresponding to row i and column j equals (r_i)(c_j)/n.

When we carry out a chi-square goodness of fit test for a normal distribution,the null hypothesis states that the population:

Consider the 3 × 2 contingency table below.What is the expected value for A₃B₁? Factor B Factor A 16 14 15 25 9 21

How many degrees of freedom are associated with the chi-square test?

An Introduction to Business Statistics

Descriptive Statistics

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Correlation Coefficient and Simple Linear Regression Analysis

Multiple Regression and Model Building

Nonparametric Methods

Decision Theory

Time Series Forecasting

Filters

Exam 14: Chi-Square Tests

Use a significance level of 0.05 and determine if the use of a cell phone and having an auto accident are independent.

At a significance level of .05,test H0: the set of 50 measurements came from a normal population.

Assume that H0: p1 = p2 = p3 = p4 = p5 = p6 = p7 is not rejected and state a one sentence managerial conclusion.

On the most recent tax cut proposal,a random sample of men and women were asked how they would cast their votes.The results are presented below: Issue: Tax cut proposal Favour Oppose Abstain Men 85 78 37 Women 118 61 25 -Calculate the chi-square statistic for this test of independence.

Consider the 3 × 2 contingency table below. Factor B Factor A 16 14 15 25 9 21 -Compute the expected frequencies in row 1.

Consider the 3 × 2 contingency table below.What is the expected value for A1B1? Factor B Factor A 16 14 15 25 9 21

At a significance level of .05,test H0: the factors A and B are independent.

At a significance level of .05,test H0: the probabilities are equal for all seven regions.

On the most recent tax cut proposal,a random sample of men and women were asked how they would cast their votes.The results are presented below: Issue: Tax cut proposal Favour Oppose Abstain Men 85 78 37 Women 118 61 25 -Determine the expected frequencies for the chi-square test of independence.

When we carry out a chi-square test of independence,if ri is row total for row i and cj is the column total for column j,then the estimated expected cell frequency corresponding to row i and column j equals (ri)(cj)/n.

When we carry out a chi-square goodness of fit test for a normal distribution,the null hypothesis states that the population:

Consider the 3 × 2 contingency table below.What is the expected value for A3B1? Factor B Factor A 16 14 15 25 9 21

How many degrees of freedom are associated with the chi-square test?

An Introduction to Business Statistics

Descriptive Statistics

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Correlation Coefficient and Simple Linear Regression Analysis

Multiple Regression and Model Building

Nonparametric Methods

Decision Theory

Time Series Forecasting

Filters

At a significance level of .05,test H₀: the set of 50 measurements came from a normal population.

Assume that H₀: p₁ = p₂ = p₃ = p₄ = p₅ = p₆ = p₇ is not rejected and state a one sentence managerial conclusion.

Consider the 3 × 2 contingency table below.What is the expected value for A₁B₁? Factor B Factor A 16 14 15 25 9 21

At a significance level of .05,test H₀: the factors A and B are independent.

At a significance level of .05,test H₀: the probabilities are equal for all seven regions.

When we carry out a chi-square test of independence,if r_i is row total for row i and c_j is the column total for column j,then the estimated expected cell frequency corresponding to row i and column j equals (r_i)(c_j)/n.

Consider the 3 × 2 contingency table below.What is the expected value for A₃B₁? Factor B Factor A 16 14 15 25 9 21