Deck 14: Chi-Square Tests

Question 1

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

Answer 1

False

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

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

Answer 3

True

Question 4

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

Question 5

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

Question 6

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

Question 7

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.

Question 8

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

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.

Question 10

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

Question 11

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 is correct.

Question 12

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

Question 13

A fastener manufacturing company uses a chi-square goodness of fit test to determine if a population of all lengths of 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 14

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

Question 15

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 16

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 set comes from other distribution forms such as Poisson.

Question 17

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

Question 18

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

Question 19

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 20

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

Question 21

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?

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

Question 22

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 normal distribution. In order to determine whether the selling prices of homes included in the random sample are normally distributed, the data is divided into 6 classes of equal size and the number of observations in each class is recorded. The chi-square goodness of fit test for normal distribution is performed and the results are summarized in the following table:
Goodness of Fit Test
$$\begin{array} { l l l l l } \text { Observed } & \text { expected } & \mathrm { O } - \mathrm { E } & ( \mathrm { O } - \mathrm { E } ) ^ { 2 } / \mathrm { E } & \% \text { of chisq } \\10 & 3.192 & 6.808 & 14.520 & 64.81 \\23 & 19.026 & 3.974 & 0.830 & 3.70 \\37 & 47.782 & -10.782 & 2.433 & 10.86 \\40 & 47.782 & -7.782 & 1.267 & 5.66\\27 & 19.026 & 7.974 & 3.342 & 14.92 \\3 & 3.192 & -0.192 & 0.012 & 0.05 \\140 & 140.000 & 0.000 & 22.404 & 100.00\\22.40 & \text { Chi-square } \\.0001 & \text { p-value }\end{array}$$

-What is the appropriate null hypothesis?

A)H₀: The residential home selling prices are distributed according to normal distribution.
B)H₀: The residential home selling prices are not distributed according to 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.

Question 23

A chi-square analysis is conducted for men and women separately to assess if the relationship found is different for the two groups.In this type of situation,sex is acting as a(n)_____.

A)binomial experiment
B)control variable
C)normal variable
D)population variance
E)exceptional factor

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, 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 ?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 25

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.
$\text { Chi-square Contingency Table Test for Independence }$
$\begin{array}{llll}&\text { Col 1 } & \text { Col 2 } & \text { Col 3 } & \text { Total } \\\text { Row } 1 \text { Observed }&29 & 12 & 9 & 50 \\\text { Expected }&21.05 & 15.79 & 13.16 & 50.00\\\text { Row 2 Observed } & 211 & 168 & 141 & 520 \\\text { Expected } & 218.95 & 164.21 & 136.84 & 520.00\\ (\mathrm{O}-\mathrm{E})^{2} / \mathrm{E} & 0.29 & 0.09 & 0.13 & 0.50 \\\text { Total } \text { Observed } & 240 & 180 & 150 & 570\\\text { Expected } & 240.00 & 180.00 & 150.00 & 570.00 \\(\mathrm{O}-\mathrm{E})^{2} / \mathrm{E} & 3.29 & 1.00 & 1.44 & 5.73\\\\&5.73 & \text { chi-square } \\&.0571 & \mathrm{p} \text {-value }\end{array}$


-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 Mega-Stat/Excel output provided in the table above,we:

A)Reject H₀ and conclude that the quality of the product is different for all pairs of manufacturing process.
B)Reject H₀ and conclude that the quality of the product is dependent on the manufacturing process.
C)Failed to 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.

Question 26

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

A)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.
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.

Question 27

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 28

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 normal distribution. In order to determine whether the selling prices of homes included in the random sample are normally distributed, the data is divided into 6 classes of equal size and the number of observations in each class is recorded. The chi-square goodness of fit test for normal distribution is performed and the results are summarized in the following table:
Goodness of Fit Test
$$\begin{array} { l l l l l } \text { Observed } & \text { expected } & \mathrm { O } - \mathrm { E } & ( \mathrm { O } - \mathrm { E } ) ^ { 2 } / \mathrm { E } & \% \text { of chisq } \\10 & 3.192 & 6.808 & 14.520 & 64.81 \\23 & 19.026 & 3.974 & 0.830 & 3.70 \\37 & 47.782 & -10.782 & 2.433 & 10.86 \\40 & 47.782 & -7.782 & 1.267 & 5.66\\27 & 19.026 & 7.974 & 3.342 & 14.92 \\3 & 3.192 & -0.192 & 0.012 & 0.05 \\140 & 140.000 & 0.000 & 22.404 & 100.00\\22.40 & \text { Chi-square } \\.0001 & \text { p-value }\end{array}$$

-What are the degrees of freedom for the chi-square test?

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

Question 29

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 30

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 normal distribution. In order to determine whether the selling prices of homes included in the random sample are normally distributed, the data is divided into 6 classes of equal size and the number of observations in each class is recorded. The chi-square goodness of fit test for normal distribution is performed and the results are summarized in the following table:
Goodness of Fit Test
$$\begin{array} { l l l l l } \text { Observed } & \text { expected } & \mathrm { O } - \mathrm { E } & ( \mathrm { O } - \mathrm { E } ) ^ { 2 } / \mathrm { E } & \% \text { of chisq } \\10 & 3.192 & 6.808 & 14.520 & 64.81 \\23 & 19.026 & 3.974 & 0.830 & 3.70 \\37 & 47.782 & -10.782 & 2.433 & 10.86 \\40 & 47.782 & -7.782 & 1.267 & 5.66\\27 & 19.026 & 7.974 & 3.342 & 14.92 \\3 & 3.192 & -0.192 & 0.012 & 0.05 \\140 & 140.000 & 0.000 & 22.404 & 100.00\\22.40 & \text { Chi-square } \\.0001 & \text { p-value }\end{array}$$

-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 31

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

Question 32

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.

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

Question 33

The χ² statistic from a contingency table with 6 rows and 5 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 34

When we carry out a chi-square test of independence,the alternative 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 35

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.

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

Question 36

The χ² statistic is used to test to test whether the assumption of normality is reasonable for a given population distribution.The sample consists of 200 observations and is divided into 6 categories (intervals).The degrees of freedom for the chi-square statistic is:

A)199
B)6
C)5
D)4
E)3

Question 37

When we carry out a chi-square test of independence,as the difference 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 38

The chi-square goodness of fit test will be valid if each 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 39

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.
$\text { Chi-square Contingency Table Test for Independence }$
$\begin{array}{llll}&\text { Col 1 } & \text { Col 2 } & \text { Col 3 } & \text { Total } \\\text { Row } 1 \text { Observed }&29 & 12 & 9 & 50 \\\text { Expected }&21.05 & 15.79 & 13.16 & 50.00\\\text { Row 2 Observed } & 211 & 168 & 141 & 520 \\\text { Expected } & 218.95 & 164.21 & 136.84 & 520.00\\ (\mathrm{O}-\mathrm{E})^{2} / \mathrm{E} & 0.29 & 0.09 & 0.13 & 0.50 \\\text { Total } \text { Observed } & 240 & 180 & 150 & 570\\\text { Expected } & 240.00 & 180.00 & 150.00 & 570.00 \\(\mathrm{O}-\mathrm{E})^{2} / \mathrm{E} & 3.29 & 1.00 & 1.44 & 5.73\\\\&5.73 & \text { chi-square } \\&.0571 & \mathrm{p} \text {-value }\end{array}$


-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 Mega-Stat/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)Failed to reject H₀ and conclude that the quality of the product does not significantly differ among the three processes.
D)Failed to 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 40

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 appear 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)H₀: The number of defectives produced is dependent on the production process used.

Question 41

Consider the 3 × 2 contingency table below.What is the expected value for A₂B₂? $$\begin{array} { c c c } & { \text { Factor B } } \\\text { Factor A } & B _ { 1 } & B _ { 2 } \\\mathrm {~A} _ { 1 } & 16 & 14 \\\mathrm {~A} _ { 2 } & 15 & 25 \\\mathrm {~A} _ { 3 } & 9 & 21\end{array}$$

A)12
B)14
C)16
D)18
E)24

Question 42

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 normal distribution. In order to determine whether the selling prices of homes included in the random sample are normally distributed, the data is divided into 6 classes of equal size and the number of observations in each class is recorded. The chi-square goodness of fit test for normal distribution is performed and the results are summarized in the following table:
Goodness of Fit Test
$$\begin{array} { l l l l l } \text { Observed } & \text { expected } & \mathrm { O } - \mathrm { E } & ( \mathrm { O } - \mathrm { E } ) ^ { 2 } / \mathrm { E } & \% \text { of chisq } \\10 & 3.192 & 6.808 & 14.520 & 64.81 \\23 & 19.026 & 3.974 & 0.830 & 3.70 \\37 & 47.782 & -10.782 & 2.433 & 10.86 \\40 & 47.782 & -7.782 & 1.267 & 5.66\\27 & 19.026 & 7.974 & 3.342 & 14.92 \\3 & 3.192 & -0.192 & 0.012 & 0.05 \\140 & 140.000 & 0.000 & 22.404 & 100.00\\22.40 & \text { Chi-square } \\.0001 & \text { p-value }\end{array}$$

-At a significance level of .05,we:

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

Question 43

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

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

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 normal distribution. In order to determine whether the selling prices of homes included in the random sample are normally distributed, the data is divided into 6 classes of equal size and the number of observations in each class is recorded. The chi-square goodness of fit test for normal distribution is performed and the results are summarized in the following table:
Goodness of Fit Test
$$\begin{array} { l l l l l } \text { Observed } & \text { expected } & \mathrm { O } - \mathrm { E } & ( \mathrm { O } - \mathrm { E } ) ^ { 2 } / \mathrm { E } & \% \text { of chisq } \\10 & 3.192 & 6.808 & 14.520 & 64.81 \\23 & 19.026 & 3.974 & 0.830 & 3.70 \\37 & 47.782 & -10.782 & 2.433 & 10.86 \\40 & 47.782 & -7.782 & 1.267 & 5.66\\27 & 19.026 & 7.974 & 3.342 & 14.92 \\3 & 3.192 & -0.192 & 0.012 & 0.05 \\140 & 140.000 & 0.000 & 22.404 & 100.00\\22.40 & \text { Chi-square } \\.0001 & \text { p-value }\end{array}$$

-In order to study the nature of the dependency between the classifications in a contingency table,it is often useful to plot the _____.

A)row percentages
B)expected cell values
C)column percentages
D)row and/or column percentages
E)observed frequencies

Question 45

Consider the 3 × 2 contingency table below.How many degrees of freedom are associated with the chi-square test? $$\begin{array} { c c c } & { \text { Factor B } } \\\text { Factor A } & \mathrm { B } _ { 1 } & \mathrm {~B} _ { 2 } \\\mathrm {~A} _ { 1 } & 16 & 14 \\\mathrm {~A} _ { 2 } & 15 & 25 \\\mathrm {~A} _ { 3 } & 9 & 21\end{array}$$

A)2
B)4
C)6
D)8
E)10

Question 46

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

Question 47

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 interval 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 ____.

Question 48

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 _____.

Question 49

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

Question 50

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

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

Question 51

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 _____.

Question 52

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 approximately correct.

Question 53

Consider the 3 × 2 contingency table below.What is the expected value for A₂B₁? $$\begin{array} { c c c } & { \text { Factor B } } \\\text { Factor A } & B _ { 1 } & B _ { 2 } \\\mathrm{A}_{1} & 16 & 14 \\\mathrm{~A}_{2} & 15 & 25 \\\mathrm{~A}_{3} & 9 & 21\end{array}$$

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

Question 54

A ____________ is an additional factor added to the model to examine if the pattern of the data changes or stays the same when this additional factor is considered.

Question 55

Consider the 3 × 2 contingency table below.What is the expected value for A₃B₂? $$\begin{array} { c c c } &{ \text { Factor B } } \\\text { Factor A } & \mathrm { B } _ { 1 } & \mathrm {~B} _ { 2 } \\\mathrm {~A} _ { 1 } & 16 & 14 \\\mathrm {~A} _ { 2 } & 15 & 25 \\\mathrm {~A} _ { 3 } & 9 & 21\end{array}$$

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

Question 56

Consider the 3 × 2 contingency table below.What is the expected value for A₁B₂? $$\begin{array} { c c c } & { \text { Factor B } } \\\text { Factor A } & \mathrm { B } _ { 1 } & \mathrm {~B} _ { 2 } \\\mathrm {~A} _ { 1 } & 16 & 14 \\\mathrm {~A} _ { 2 } & 15 & 25 \\\mathrm {~A} _ { 3 } & 9 & 21\end{array}$$

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

Question 57

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 ______________.

Question 58

In order to study the nature of the dependency between the classifications in a contingency table,it is often useful to plot the row and/or column _________.

Question 59

Consider the 3 × 2 contingency table below.At $\alpha$
= )05,what is the tabular value of the chi-square statistic (critical chi-square value)which would be used to test for the independence of Factors A and B? $$\begin{array} { c c c } & { \text { Factor B } } \\\text { Factor A } & \mathrm { B } _ { 1 } & \mathrm {~B} _ { 2 } \\\mathrm {~A} _ { 1 } & 16 & 14 \\\mathrm {~A} _ { 2 } & 15 & 25 \\\mathrm {~A} _ { 3 } & 9 & 21\end{array}$$

A)0100
B)0201
C)5.991
D)5.024
E)10.597

Question 60

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? $$\begin{array} { l c c } \text { Interval } & \text { Observed Frequencies } & \text { Expected frequencies } \\39.99 \text { and less } & 12 & 14.56 \\40 - 59.99 & 18 & 20.365 \\60 - 79.99 & 15 & 12.28 \\80 \text {-and higher } & 5 & 2.795\end{array}$$

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

Question 61

At a significance level of .01,test H₀: the probabilities are equal for all seven regions.

Question 62

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

Question 63

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

Question 64

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.
Calculate the expected enrolment (frequency)for all 7 regions (hint: p₁ = p₂ = p₃ = p₄ = p₅ = p₆ = p₇).

Question 65

Consider a set of 50 measurements with a mean of 50.2 and a standard deviation of 18.7 and with the following observed and expected frequencies. It is desired to test whether these measurements came from a normal population.
Calculate the value of the chi-square test statistic?

Question 66

At = .05,determine the tabular value of the chi-square statistic used to test for the independence of Factors A and B?

Question 67

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed frequencies. It is desired to test whether these measurements came from a normal population.
Calculate the expected frequency for the interval 0-39.99.

Question 68

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed frequencies. It is desired to test whether these measurements came from a normal population.
Calculate the expected frequency for the interval 60 - 79.99.

Question 69

Consider the 3 × 2 contingency table below.


-Compute the expected frequencies in row 1.

Question 70

How many degrees of freedom are associated with the chi-square test? Use α = .05 and determine the rejection point condition of the chi-square statistic.

Question 71

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

Question 72

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 ___________.

Question 73

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

Question 74

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

Question 75

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed frequencies. It is desired to test whether these measurements came from a normal population.
Calculate the expected frequency for the interval 40 - 59.99.

Question 76

Consider the 3 × 2 contingency table below.


-Compute the expected frequencies in row 2.

Question 77

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed frequencies. It is desired to test whether these measurements came from a normal population.
Calculate the expected frequency for the interval 80 and higher.

Question 78

Assume that H₀: p₁ = p₂ = p₃ = p₄ = p₅ = p₆ = p₇ is rejected.State a one sentence managerial conclusion.

Question 79

Consider the 3 × 2 contingency table below.


-Compute the expected frequencies in row 3.

Question 80

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.
Calculate the value of the chi-square statistic.