Question 1

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 in a goodness of fit chi-square test are based on the null hypothesis, not the alternative hypothesis. The null hypothesis represents the theoretical distribution that we are comparing our observed data to, and the expected frequencies are calculated based on this distribution.

Question 2

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

For a chi-square goodness of fit test with k intervals, the degrees of freedom for the chi-square statistic is given by (k - 1). Therefore, for 7 intervals, the degrees of freedom would be (7 - 1) = 6. Hence, the correct option is (C).

Question 3

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 observed and expected frequencies decrease, it means that the observed and expected frequencies are becoming more similar. This suggests that the row variable and column variable are becoming more independent. Therefore, the probability of concluding that the row variable is independent of the column variable increases.

Question 4

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 5

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 6

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 7

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

Accepted Answer

The degrees of freedom for a chi-square goodness fit test is equal to the number of intervals minus 1. In this case, the researcher has 7 intervals, but the first and last intervals have expected cell frequencies of less than 5, so they are combined into one interval. This leaves the researcher with 6 intervals, and the degrees of freedom for the chi-square statistic is 6 - 1 = 5.

Question 8

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. Therefore, option B is the correct answer. Option A is incorrect because it goes against the null hypothesis. Option C is incorrect because the hypothesis is about the normal distribution, not the chi-square distribution. Option D is also incorrect for the same reason. Option E is irrelevant to this hypothesis test.

Question 9

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 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

In a chi-square goodness of fit test with multinomial probabilities, the test statistic is calculated as the sum of the squared differences between observed and expected frequencies divided by the expected frequencies. Therefore, a larger difference between observed and expected frequencies will result in a larger test statistic and a lower probability of concluding that the probabilities specified in the null hypothesis are correct. Thus, smaller differences between observed and expected frequencies will result in a higher probability of concluding that the probabilities specified in the null hypothesis are correct.

Question 11

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.

Question 12

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 is specifically used for count data that can be classified into more than two mutually exclusive categories. This is in contrast to a binomial distribution which only has two categories. Therefore, choice D is the best answer.

Question 13

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

The chi-square goodness of fit test assumes that the expected cell frequencies are at least 5. This ensures that the chi-square distribution accurately approximates the true distribution of the test statistic. If the expected frequencies are less than 5, then the test may be unreliable and the results may not be valid. Therefore, the best choice is E, which indicates that the average of the expected cell frequencies is at least 5.

Question 14

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 15

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 16

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 chi-square goodness of fit test is always a one-tailed test with the rejection region in the right tail because it tests whether the observed frequencies deviate significantly from the expected frequencies, which would result in a large chi-square statistic.

Question 17

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 special version of 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 homogeneity. The other options listed are different types of statistical tests.

Question 18

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.

Accepted Answer

The answer of The χ² statistic from a contingency table...

Question 19

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

Question 20

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

Accepted Answer

The larger the difference between observed and expected frequency, the less likely it is due to chance and the more likely it is due to a significant relationship. Therefore, as the difference between observed and expected frequency increases, the probability of rejecting the null hypothesis increases.

Quiz 13: Chi-Square Tests

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

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:

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 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 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 _____.

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.

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

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.

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

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 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 ___________.

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

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

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

Quiz 13: Chi-Square Tests

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

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:

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 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 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 _____.

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.

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

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.

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

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 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 ___________.

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

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

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

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:

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