Question 1

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

Accepted Answer

The null hypothesis for a chi-square test of independence states that the two relevant classifications are statistically independent, which is the opposite of being statistically dependent. Therefore, choice D is the correct answer. A, B, C, and E are either unrelated to the null hypothesis or incorrect.

Question 2

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

Accepted Answer

The expected number of defective units for Process 1 is calculated using the formula for expected frequency in a contingency table: (Row Total * Column Total) / Grand Total. Here, the expected number of defective units for Process 1 is (240 * 50) / 570 = 21.053.

Question 3

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 $\chi$² > .10257 B)Reject H₀ if $\chi$² > 9.3484 C)Reject H₀ if $\chi$² > 5.99147 D)Reject H₀ if $\chi$² > 7.37776 E)Reject H₀ if $\chi$² > 7.81473

Accepted Answer

Since we are comparing the quality of three different production processes, we can use a chi-square goodness-of-fit test. The null hypothesis (H0) would be that the quality is the same for all three processes, and the alternative hypothesis (Ha) would be that the quality is different for at least one process.
The rejection point for this test can be found using a chi-square distribution table with degrees of freedom (df) equal to the number of categories minus 1 (df = 3-1 = 2) and a significance level (α) of 0.05. From the table, the critical value is 5.99147.
Therefore, we can reject H0 if the calculated chi-square statistic is greater than 5.99147.

Question 4

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

Accepted Answer

The general rule of thumb is that each expected cell frequency should be at least 5 for the chi-square goodness of fit test to be valid. This gives enough data for the test to be reliable and accurate. Therefore, choice E (at least 5) is the best option.

Question 5

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 appears 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

Accepted Answer

The degrees of freedom for the chi-square test of independence is calculated as df = (number of rows - 1) x (number of columns - 1). In this case, there are 3 processes and 2 outcomes (defective and non-defective), so df = (3-1) x (2-1) = 2. Therefore, the answer is choice letter B.

Question 6

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

Accepted Answer

As the difference between the observed and expected frequencies decreases, the chi-square test statistic decreases as well, and the probability of concluding that the row variable is independent of the column variable increases. This is because smaller values of the test statistic indicate that the observed data are closer to what would be expected if the variables were independent, increasing the likelihood of failing to reject the null hypothesis (i.e., concluding that the variables are independent).

Question 7

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 n the contingency table. D)The alternative hypothesis states that the two classifications are statistically independent. E)All of the above statements are true about the chi-square test of independence.

Accepted Answer

The alternative hypothesis for the chi-square test of independence states that the two classifications are not statistically independent, meaning there is an association between them.

Question 8

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

Accepted Answer

The answer of A manufacturing company produces part 2205 for...

Question 9

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

Accepted Answer

In the chi-square goodness-of-fit test, expected frequencies are based on the null hypothesis.

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: The 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)Both A and C are correct or at least acceptable way of stating the null hypothesis. E)A,B and C are all acceptable ways of stating the null hypothesis.

Accepted Answer

The answer of A manufacturing company produces part 2205 for...

Question 11

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

Accepted Answer

The null hypothesis in a chi-square goodness of fit test for a normal distribution states that the population has a normal distribution.

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: The 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 .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 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)Reject H₀ and conclude that the quality of the product is independent of the production process utilized. E)Both A and B are correct.

Accepted Answer

The answer of A manufacturing company produces part 2205 for...

Question 13

The chi-square goodness of fit test can be used when:
A)We conduct a binomial experiment.
B)We conduct a multinomial experiment.
C)We perform a hypothesis test to determine if a population has a normal distribution.
D)We perform a hypothesis test to determine if two population variances significantly differ from each other.

Accepted Answer

The chi-square goodness of fit test is used to determine whether an observed frequency distribution is significantly different from an expected frequency distribution when the variable is categorical with more than two categories. In other words, it is used for multinomial experiments with categorical data. Therefore, option B is the best choice. Options A, C, and D are not correct because they refer to different types of hypothesis tests that use different statistical methods.

Question 14

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: The 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 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.

Accepted Answer

The answer of A manufacturing company produces part 2205 for...

Question 15

A real estate company is analyzing the selling prices of residential homes in a given community.140 homes that have been solved 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:  What are the degrees of freedom for the chi-square test?
A)2
B)3
C)4
D)5
E)6

Accepted Answer

The answer of A real estate company is analyzing the...

Question 16

A real estate company is analyzing the selling prices of residential homes in a given community.140 homes that have been solved 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: 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. E)None of the above is correct.

Accepted Answer

The answer of A real estate company is analyzing the...

Question 17

The $\chi$² 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

Accepted Answer

The formula to calculate degrees of freedom for a chi-square test of independence is:
(df) = (number of rows - 1) x (number of columns - 1)

Using this formula, we get:
(df) = (6-1) x (5-1) = 20

Therefore, the answer is D) 20 degrees of freedom.

Question 18

A real estate company is analyzing the selling prices of residential homes in a given community.140 homes that have been solved 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: At a significance level of .05,what is the appropriate rejection point condition? A)Reject H₀ if $\chi$² > 12.5916 B)Reject H₀ if $\chi$² > 11.0705 C)Reject H₀ if $\chi$² > 9.3484 D)Reject H₀ if $\chi$² > 7.81473 E)Reject H₀ if $\chi$² > 9.48773

Accepted Answer

The answer of A real estate company is analyzing the...

Question 19

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

Accepted Answer

The answer of The chi-square goodness of fit is _________...

Question 20

The $\chi$² 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

Accepted Answer

The answer of The $\chi$² statistic is used to test...

Quiz 12: Chi-Square Tests

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

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

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:

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

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

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

The chi-square goodness of fit test can be used when:

The $\chi$ ² statistic from a contingency table with 6 rows and five columns will have

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

The $\chi$ ² 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:

Quiz 12: Chi-Square Tests

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

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

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:

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

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

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

The chi-square goodness of fit test can be used when:

The χ\chiχ 2 statistic from a contingency table with 6 rows and five columns will have

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

The χ\chiχ 2 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 $\chi$ ² statistic from a contingency table with 6 rows and five columns will have

The $\chi$ ² 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: