Question 1

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

Accepted Answer

For the chi-square goodness-of-fit test to be valid, the expected cell frequency should be at least 5. This ensures that the assumptions of the test are met and that the results can be trusted. Therefore, choice E (at least 5) is the correct answer.

Question 2

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

Accepted Answer

df = (4 − 1)(3 − 1) = 6

Question 3

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

Accepted Answer

A multinomial distribution describes count data that are classified into more than two mutually exclusive categories.

Question 4

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

Accepted Answer

(0.25)(400) = 100

Question 5

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.

Accepted Answer

Degrees of freedom = (6 − 1)(5 − 1) = 5 × 4 = 20

Question 6

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

This is because the chi-square distribution is skewed to the right.

Question 7

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

Accepted Answer

The test for homogeneity is used to determine if two or more populations have the same proportion of individuals falling into different categories. It is a special version of the chi-square goodness-of-fit test and is often used in survey research or clinical trials to compare the response rates of different groups.

Question 8

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.

Accepted Answer

The alternate hypothesis in a chi-square test of independence states that the two relevant classifications are statistically dependent. The other choices are either not relevant to the hypothesis or inaccurate. Therefore, the correct answer is D.

Question 9

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.

Accepted Answer

The alternative hypothesis in a chi-square test of independence states that the two classifications are not statistically independent.

Question 10

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

Accepted Answer

A smaller difference between observed and expected frequencies indicates a better fit between the data and the null hypothesis, and therefore a higher probability of concluding that the specified probabilities are correct.

Question 11

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.

Accepted Answer

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

Question 12

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)goes to 0

Accepted Answer

The larger the difference between observed frequency and expected frequency, the less likely it is that the difference is due to chance alone. Thus, the probability of rejecting the null hypothesis increases as the difference between observed frequency and expected frequency increases.

Question 13

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

Accepted Answer

The degrees of freedom for a chi-square goodness-of-fit test for a normal distribution with k intervals is k-3. Therefore, in this case, the degrees of freedom will be 7-3 = 4. Option C is the correct answer.

Question 14

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.

Accepted Answer

As the differences between the respective observed and expected frequencies decrease, the chi-square test value decreases, leading to a higher probability of concluding that the row variable is independent of the column variable. Lower chi-square test values indicate less deviation from independence and, therefore, a higher probability of independence.

Question 15

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

Accepted Answer

The expected frequencies are based on the null hypothesis in a goodness-of-fit chi-square test. The alternative hypothesis is used to determine which distribution the observed data may follow.

Question 16

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

Accepted Answer

5 − 1 = 4

Question 17

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

Question 18

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

Accepted Answer

Degrees of freedom = k − 3, where k = number of intervals. Thus, df = 6 − 3 = 3

Question 19

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

Accepted Answer

If there is a small or negligible difference between the observed and expected frequencies, then it means there is a small probability that you will reject the null.

Question 20

In performing a chi-square goodness-of-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

Accepted Answer

The researcher needs to combine the 1st and 2nd intervals together and the 6th and 7th intervals together, because of small frequencies in the 1st and 6th. The new degrees of freedom = 5 − 3 = 2.

Quiz 12: Chi-Square Tests

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

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 _____.

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.

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 _____.

The χ² statistic from a contingency table with 6 rows and 5 columns will have:

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

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 ___________.

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

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

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.

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

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 ______________.

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:

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

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

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

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:

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.

Quiz 12: Chi-Square Tests

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

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 _____.

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.

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 _____.

The χ2 statistic from a contingency table with 6 rows and 5 columns will have:

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

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 ___________.

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

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

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.

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

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 ______________.

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:

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

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

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

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:

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.

The χ² statistic from a contingency table with 6 rows and 5 columns will have:

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: