Deck 13: Chi-Square Tests

Question 1

When we carry out a chi-square test of independence,the expected frequencies are based on the null hypothesis.

Answer 1

True

Question 2

When using a chi-square goodness of fit test with multinomial probabilities,the rejection of the null hypothesis indicates that at least one of the multinomial probabilities is not equal to the value stated in the null hypothesis.

Answer 2

True

Question 3

The χ² goodness of fit test requires the nominative level of data.

Answer 3

True

Question 4

In performing a chi-square test of independence,as the difference between the respective observed and expected frequencies decreases,the probability of concluding that the row variable is independent of the column variable decreases.

Question 5

When we carry out a chi-square test of independence,in the alternative hypothesis we state that the two classifications are statistically independent.

Question 6

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.

Question 7

A multinomial probability distribution describes data that are classified into two or more categories when a multinomial experiment is carried out.

Question 8

When we carry out a chi-square test of independence,if r_i is the 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.

Question 9

When using the chi-square goodness of fit test,if the value of the chi-square statistic is large enough,we reject the null hypothesis.

Question 10

The chi-square goodness of fit test can only be used to test whether a population has specified multinomial probabilities or to test if a sample has been selected from a normally distributed population.It cannot be applied to test if a sample data comes from other distribution forms such as the Poisson.

Question 11

A contingency table summarizes data that has been classified on two dimensions or scales.

Question 12

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.

Question 13

Expected cell frequencies for a multinomial distribution are calculated by assuming statistical dependence.

Question 14

The actual counts in the cells of a contingency table are referred to as the expected cell frequencies.

Question 15

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.

Question 16

In a contingency table,when all the expected frequencies equal the observed frequencies,the calculated χ² statistic equals zero.

Question 17

The trials of a multinomial probability are assumed to be dependent.

Question 18

The chi-square distribution is a continuous probability distribution that is skewed to the left.

Question 19

One use of the chi-square goodness of fit test is to determine if specified multinomial probabilities in the null hypothesis are correct.

Question 20

In performing a chi-square goodness of fit test with multinomial probabilities,the smaller the difference between observed and expected frequencies,the higher the probability of concluding that the probabilities specified in the null hypothesis are correct.

Question 21

When we carry out a goodness of fit chi-square test,the expected frequencies are based on the alternative hypothesis.

Question 22

In performing a chi-square goodness of fit test for a normal distribution,if there are 7 intervals,then the degrees of freedom for the chi-square statistic is ______________.

A)7
B)3
C)4
D)6

Question 23

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:

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

Question 24

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 a chi-square test to determine whether the quality of the items produced appears to be the same for all three processes.What is the null hypothesis?

A)H₀: The number of defectives produced is independent of the production process used.
B)H₀: The row and column variables are associated with each other.
C)H₀: The proportion of defective units produced by the three production processes is the same.
D)Both H₀: The number of defectives produced is independent of the production process used and H₀: The proportion of defective units produced by the three production processes is the same are correct or at least acceptable ways of stating the null hypothesis.
E)H₀: The number of defectives produced is independent of the production process used,H₀: The row and column variables are associated with each other,and H₀: The proportion of defective units produced by the three production processes is the same are all acceptable ways of stating the null hypothesis.

Question 25

An experiment consists of 400 observations and four mutually exclusive groups.If the probability of a randomly selected item being classified into any of the four groups is equal,then the expected number of items that will be classified into group 1 is _____.

A)25
B)100
C)125
D)150

Question 26

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

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

Question 27

In performing a chi-square goodness fit test for a normal distribution,a researcher wants to make sure that all of the expected cell frequencies are at least five.The sample is divided into 7 intervals.The second through the sixth intervals all have expected cell frequencies of at least five.The first and the last intervals have expected cell frequencies of 1.5 each.After adjusting the number of intervals,the degrees of freedom for the chi-square statistic is ____.

A)2
B)3
C)5
D)7

Question 28

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

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 29

The number of degrees of freedom associated with a chi-square test for independence based upon a contingency table with 4 rows and 3 columns is _____.

A)7
B)12
C)5
D)6

Question 30

In performing a chi-square goodness of fit test with multinomial probabilities,the ___________ the difference between observed and expected frequencies,the higher the probability of concluding that the probabilities specified in the null hypothesis are correct.

A)larger
B)smaller

Question 31

When we carry out a chi-square test of independence,the alternate hypothesis states that the two relevant classifications:

A)Are mutually exclusive.
B)Form a contingency table with r rows and c columns.
C)Have (r - 1)(c - 1)degrees of freedom.
D)Are statistically dependent.
E)Are normally distributed.

Question 32

While a binomial distribution describes count data that can be classified into one of two mutually exclusive categories,a __________________ distribution describes count data that are classified into more than two mutually exclusive categories.

A)normal
B)skewed
C)uniform
D)multinomial

Question 33

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

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

Question 34

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:

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

Question 35

In performing a chi-square test of independence,as the differences between respective observed and expected frequencies _________,the probability of concluding that the row variable is independent of the column variable increases.

A)stay the same
B)decrease
C)increase
D)double

Question 36

The chi-square goodness of fit is _________ a one-tailed test with the rejection region in the right tail.

A)Always
B)Sometimes
C)Never

Question 37

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 ___________.

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

Question 38

The χ² statistic from a contingency table with 6 rows and five columns will have:

A)30 degrees of freedom.
B)24 degrees of freedom.
C)5 degrees of freedom.
D)20 degrees of freedom.
E)25 degrees of freedom.

Question 39

Which,if any,of the following statements about the chi-square test of independence is false?

A)If r_i is the 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.
B)The test is valid if all of the estimated cell frequencies are at least five.
C)The chi-square statistic is based on (r - 1)(c - 1)degrees of freedom,where r and c denote,respectively,the number of rows and columns in the contingency table.
D)The alternative hypothesis states that the two classifications are statistically independent.
E)All of these statements are true about the chi-square test of independencE.

Question 40

As the difference between observed frequency and expected frequency _______________,the probability of rejecting the null hypothesis increases.

A)stays the same
B)decreases
C)increases
D)go to 0

Question 41

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.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?

A)Reject H₀ if χ² > .10257
B)Reject H₀ if χ² > 9.3484
C)Reject H₀ if χ² > 5.99147
D)Reject H₀ if χ² > 7.37776
E)Reject H₀ if χ² > 7.81473

Question 42

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:

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 43

Consider the 3 × 2 contingency table below.

Question 44

A real estate company is analyzing the selling prices of residential homes in a given community.140 homes that have been sold in the past month are randomly selected and their selling prices are recorded.The statistician working on the project has stated that in order to perform various statistical tests,the data must be distributed according to a normal distribution.In order to determine whether the selling prices of homes included in the random sample are normally distributed,the statistician divides the data into 6 classes of equal size and records the number of observations in each class.She then performs a chi-square goodness of fit test for normal distribution.The results are summarized in the following table.
Goodness of Fit Test $$\begin{array} { r | r | r | r | r } \text { Observed } & \text { Expected } & \mathrm { O } - \mathrm { E } & ( \mathrm { O } - \mathrm { E } ) ^ { 2 } \mathrm { E } & \% \text { of chi-square } \\\hline 10 & 3.192 & 6.808 & 14.520 & 64.81 \\\hline 23 & 19.026 & 3.974 & 0.830 & 3.70 \\\hline 37 & 47.782 & - 10.782 & 2.433 & 10.86 \\\hline 40 & 47.782 & - 7.782 & 1.267 & 5.66 \\\hline 27 & 19.026 & 7.974 & 3.342 & 14.92 \\\hline 3 & 3.192 & - 0.192 & 0.012 & 0.05 \\\hline 140 & 140.000 & 0.000 & 22.404 & 100.00 \\\hline & & & & \\\hline 22.40 & \text { chi-square } & & & \\\hline .0001 & \text { p-value } & & &\end{array}$$
At a significance level of .05,what is the appropriate rejection point condition?

A)Reject H₀ if ?² > 12.5916
B)Reject H₀ if ?² > 11.0705
C)Reject H₀ if ?² > 9.3484
D)Reject H₀ if ?² > 7.81473
E)Reject H₀ if ?² > 9.48773

Question 45

Consider the 3 × 2 contingency table below.

Question 46

A real estate company is analyzing the selling prices of residential homes in a given community.140 homes that have been sold in the past month are randomly selected and their selling prices are recorded.The statistician working on the project has stated that in order to perform various statistical tests,the data must be distributed according to a normal distribution.In order to determine whether the selling prices of homes included in the random sample are normally distributed,the statistician divides the data into 6 classes of equal size and records the number of observations in each class.She then performs a chi-square goodness of fit test for normal distribution.The results are summarized in the following table.
Goodness of Fit Test $$\begin{array} { r | r | r | r | r } \text { Observed } & \text { Expected } & \mathrm { O } - \mathrm { E } & ( \mathrm { O } - \mathrm { E } ) ^ { 2 } \mathrm { E } & \% \text { of chi-square } \\\hline 10 & 3.192 & 6.808 & 14.520 & 64.81 \\\hline 23 & 19.026 & 3.974 & 0.830 & 3.70 \\\hline 37 & 47.782 & - 10.782 & 2.433 & 10.86 \\\hline 40 & 47.782 & - 7.782 & 1.267 & 5.66 \\\hline 27 & 19.026 & 7.974 & 3.342 & 14.92 \\\hline 3 & 3.192 & - 0.192 & 0.012 & 0.05 \\\hline 140 & 140.000 & 0.000 & 22.404 & 100.00 \\\hline & & & & \\\hline 22.40 & \text { chi-square } & & & \\\hline .0001 & \text { p-value } & & &\end{array}$$
What are the degrees of freedom for the chi-square test?

A)2
B)3
C)4
D)5
E)6

Question 47

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

Question 48

A real estate company is analyzing the selling prices of residential homes in a given community.140 homes that have been sold in the past month are randomly selected and their selling prices are recorded.The statistician working on the project has stated that in order to perform various statistical tests,the data must be distributed according to a normal distribution.In order to determine whether the selling prices of homes included in the random sample are normally distributed,the statistician divides the data into 6 classes of equal size and records the number of observations in each class.She then performs a chi-square goodness of fit test for normal distribution.The results are summarized in the following table.
Goodness of Fit Test $$\begin{array} { r | r | r | r | r } \text { Observed } & \text { Expected } & \mathrm { O } - \mathrm { E } & ( \mathrm { O } - \mathrm { E } ) ^ { 2 } \mathrm { E } & \% \text { of chi-square } \\\hline 10 & 3.192 & 6.808 & 14.520 & 64.81 \\\hline 23 & 19.026 & 3.974 & 0.830 & 3.70 \\\hline 37 & 47.782 & - 10.782 & 2.433 & 10.86 \\\hline 40 & 47.782 & - 7.782 & 1.267 & 5.66 \\\hline 27 & 19.026 & 7.974 & 3.342 & 14.92 \\\hline 3 & 3.192 & - 0.192 & 0.012 & 0.05 \\\hline 140 & 140.000 & 0.000 & 22.404 & 100.00 \\\hline & & & & \\\hline 22.40 & \text { chi-square } & & & \\\hline .0001 & \text { p-value } & & &\end{array}$$
At a significance level of .05,we:

A)Reject H₀;conclude the residential home selling prices are not distributed according to a normal distribution.
B)Do not reject H₀;conclude the residential home selling prices are not distributed according to a normal distribution.
C)Reject H₀;conclude the residential home selling prices are distributed according to a normal distribution.
D)Do not reject H₀;conclude the residential home selling prices are distributed according to a normal distribution.

Question 49

A real estate company is analyzing the selling prices of residential homes in a given community.140 homes that have been sold in the past month are randomly selected and their selling prices are recorded.The statistician working on the project has stated that in order to perform various statistical tests,the data must be distributed according to a normal distribution.In order to determine whether the selling prices of homes included in the random sample are normally distributed,the statistician divides the data into 6 classes of equal size and records the number of observations in each class.She then performs a chi-square goodness of fit test for normal distribution.The results are summarized in the following table.
Goodness of Fit Test $$\begin{array} { r | r | r | r | r } \text { Observed } & \text { Expected } & \mathrm { O } - \mathrm { E } & ( \mathrm { O } - \mathrm { E } ) ^ { 2 } \mathrm { E } & \% \text { of chi-square } \\\hline 10 & 3.192 & 6.808 & 14.520 & 64.81 \\\hline 23 & 19.026 & 3.974 & 0.830 & 3.70 \\\hline 37 & 47.782 & - 10.782 & 2.433 & 10.86 \\\hline 40 & 47.782 & - 7.782 & 1.267 & 5.66 \\\hline 27 & 19.026 & 7.974 & 3.342 & 14.92 \\\hline 3 & 3.192 & - 0.192 & 0.012 & 0.05 \\\hline 140 & 140.000 & 0.000 & 22.404 & 100.00 \\\hline & & & & \\\hline 22.40 & \text { chi-square } & & & \\\hline .0001 & \text { p-value } & & &\end{array}$$
What is the appropriate null hypothesis?

A)H₀: The residential home selling prices are distributed according to a normal distribution.
B)H₀: The residential home selling prices are not distributed according to a normal distribution.
C)H₀: The distribution of residential home selling prices is either right or left skewed.
D)H₀: The distribution of the residential home selling prices is symmetric.
E)None of these is correct.

Question 50

Consider the 3 × 2 contingency table below.

Question 51

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 .05,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:

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)Do not reject H₀,and conclude that the quality of the product is not the same for all processes.
E)Reject H₀ and conclude that the quality of the product is independent of the manufacturing process used.

Question 52

Consider the 3 × 2 contingency table below.

Question 53

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.At a significance level of .05,we performed a chi-square test of independence to determine if the quality of the items produced appears to be independent of the production process.What are the degrees of freedom for the chi-square statistic?

A)2
B)3
C)50
D)520
E)570

Question 54

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

Question 55

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

Question 56

Consider the 3 × 2 contingency table below.

Question 57

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

Question 58

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

Question 59

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

Question 60

Consider the 3 × 2 contingency table below.

Question 61

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.Use α = .05 and determine the appropriate degrees of freedom and the rejection point condition associated with this goodness of fit test.

Question 62

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.

Question 63

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.At α = .05,test to determine if the grade distribution for Dr.Johnson's class is different from the historical grade distribution.

Question 64

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.

Question 65

On the most recent tax cut proposal,a random sample of Democrats and Republicans in the Congress cast their votes as follows:

Question 66

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.

Question 67

On the most recent tax cut proposal,a random sample of Democrats and Republicans in the Congress cast their votes as follows:

Question 68

On the most recent tax cut proposal,a random sample of Democrats and Republicans in the Congress cast their votes as follows:

Question 69

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.If we assume at α = .05 that the null hypothesis is rejected,make a one-sentence managerial conclusion.

Question 70

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.

Question 71

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.

Question 72

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.

Question 73

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.

Question 74

On the most recent tax cut proposal,a random sample of Democrats and Republicans in the Congress cast their votes as follows:

Question 75

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 expected values for B's and C's.

Question 76

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.

Question 77

On the most recent tax cut proposal,a random sample of Democrats and Republicans in the Congress cast their votes as follows:

Question 78

On the most recent tax cut proposal,a random sample of Democrats and Republicans in the Congress cast their votes as follows:

Question 79

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 expected values for A's and D's.

Question 80

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