Question 1

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 2

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 alternative would state that population is not normally distributed.

Question 3

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

If the observed frequency is much larger than the expected frequency, that means there is a large difference between the two and a higher probability of rejecting the null.

Question 4

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 5

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 null hypothesis for a chi-square test for independence is that the two classifications are statistically independent.

Question 6

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.

Question 7

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

The trials in the experiment are independent of one another.

Question 8

The χ² statistic is used to test whether the assumption of normality is reasonable for a given population distribution. The sample consists of 5,000 observations and is divided into 6 categories (intervals). The degrees of freedom for the chi-square statistic are A) 4,999. 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 9

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

Homogeneity evaluates all of the probabilities are the same or equal.

Question 10

In performing a chi-square goodness-of-fit test for a normal distribution, if there are 7 intervals, then the number of degrees of freedom for the chi-square statistic is ________.
A) 7
B) 3
C) 4
D) 6

Accepted Answer

df = 7 − 3 = 4

Question 11

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 12

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 13

A manufacturing company produces part QV2Y 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 QV2Y 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 0.05, 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) All of the other choices are acceptable ways of stating the null hypothesis.

Accepted Answer

This is a test for independence; the number of errors or defects, and not the proportion, is independent of the process used.

Question 14

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 the other statements about the chi-square test of independence are true.

Accepted Answer

The alternative hypothesis states that the two classifications are dependent.

Question 15

The chi-square goodness-of-fit test will be valid if the average of all 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

This is based on the concept of the sample size, n, being large. The sample size, n, is considered large if all of the expected cell frequencies are at least 5.

Question 16

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

When a chi-square test for independence is large (observed frequencies differ substantially from the expected frequencies), then doubt will be cast on the null hypothesis of independence. Therefore, a small difference will result in a small chi-square and lowers the likelihood of rejecting the null hypothesis of independence.

Question 17

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 18

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 favored over the alternative hypothesis.
A) larger
B) smaller

Accepted Answer

This means you have a very small likelihood of rejecting the null hypothesis.

Question 19

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 20

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.

Quiz 13: Chi-Square Tests

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

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

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

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 ________.

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 χ² statistic is used to test whether the assumption of normality is reasonable for a given population distribution. The sample consists of 5,000 observations and is divided into 6 categories (intervals) . The degrees of freedom for the chi-square statistic are

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 ________.

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

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

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.

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

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

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 favored over 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 goodness-of-fit chi-square test, the expected frequencies are based on the alternative hypothesis.

Quiz 13: Chi-Square Tests

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

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

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

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 ________.

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 χ2 statistic is used to test whether the assumption of normality is reasonable for a given population distribution. The sample consists of 5,000 observations and is divided into 6 categories (intervals) . The degrees of freedom for the chi-square statistic are

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 ________.

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

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

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.

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

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

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 favored over 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 goodness-of-fit chi-square test, the expected frequencies are based on the alternative hypothesis.

The χ² statistic is used to test whether the assumption of normality is reasonable for a given population distribution. The sample consists of 5,000 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 5 columns will have