Question 1

If we want to conduct a two-tail test of a population proportion, we can employ: A)z-test of a population proportion. B)the chi-squared test of a binomial experiment since z² = $\chi$². C)the chi-squared test of a contingency table. D)Both a and b

Accepted Answer

The answer of If we want to conduct a two-tail...

Question 2

If we want to conduct a one-tail test of a population proportion, we can employ: A)z-test of a population proportion. B)the chi-squared test of a binomial experiment since z² = $\chi$². C)the chi-squared test of a contingency table. D)Both a and b

Accepted Answer

A z-test of a population proportion is appropriate for conducting a one-tail test of a population proportion. The chi-squared test of a binomial experiment and the chi-squared test of a contingency table are not appropriate for this type of hypothesis test.

Question 3

The squared difference between the observed and expected frequencies should be large if there is a significant difference between the proportions.

Accepted Answer

This is because the chi-squared test relies on calculating the sum of squared differences between observed and expected frequencies in order to determine if there is a significant difference between proportions. A larger difference between the observed and expected frequencies indicates a larger deviation from what would be expected if the proportions were equal, and thus a greater likelihood of statistical significance.

Question 4

Which of the following tests is used to analyze nominal data? A)The z-test for one proportion, p, or difference of two proportions, p₁ - p₂. B)The chi-squared goodness-of-fitness test. C)The chi-squared test of a contingency table. D)All of these choices are true.

Accepted Answer

The answer of Which of the following tests is used...

Question 5

When we test for differences between two populations of nominal data with two categories, we can use only one technique, namely, the chi-squared test of a contingency table.

Accepted Answer

Other techniques, such as Fisher's exact test, can also be used for analyzing differences between two populations of nominal data with two categories, especially when sample sizes are small.

Question 6

Which of the following tests is appropriate for nominal data if the problem objective is to compare two populations and the number of categories exceeds 2? A)The z-test for one proportion, p, or difference of two proportions, p₁ - p₂. B)The chi-squared goodness-of-fit test. C)The chi-squared test of a contingency table. D)All of these choices are true.

Accepted Answer

The chi-squared test of a contingency table is appropriate for nominal data when comparing two populations with more than two categories. The z-test for one proportion or difference of two proportions is used for comparing proportions in binary data, while the chi-squared goodness-of-fit test is used for comparing expected and observed frequencies in one population. Therefore, the correct option is C.

Question 7

If we want to perform a one-tail test for differences between two populations of nominal data with exactly two categories, we must employ the z-test of p₁ -p₂.

Accepted Answer

The answer of If we want to perform a one-tail...

Question 8

Which of the following statements is true for chi-squared tests?
A)Testing for equal proportions is identical to testing for goodness-of-fit.
B)The number of degrees of freedom in a test of a contingency table with r rows and c columns is (r - 1)(c - 1).
C)The number of degrees of freedom in a goodness-of-fit test with k categories is k - 1.
D)All of these choices are true.

Accepted Answer

The answer of Which of the following statements is true...

Question 9

Which of the following tests is appropriate for nominal data if the problem objective is to compare two or more populations and the number of categories is at least 2? A)The z-test for one proportion, p, or difference of two proportions, p₁ - p₂. B)The chi-squared goodness-of-fitness test. C)The chi-squared test of a contingency table. D)All of these choices are true.

Accepted Answer

The chi-squared test of a contingency table is appropriate for nominal data when the objective is to compare two or more populations with at least two categories. The other options are specific to testing proportions and would not be appropriate for comparing multiple populations with nominal data.

Question 10

If we want to perform a two-tail test for differences between two populations of nominal data with exactly two categories, we can employ either the z-test of p₁ - p₂, or the chi-squared test of a contingency table.

Accepted Answer

Both the z-test and chi-squared test can be used to test for differences between two populations of nominal data with two categories. The z-test is used when the sample size is large, while the chi-squared test is used when the sample size is small to moderate. Both tests are two-tailed, meaning they test for differences in either direction.

Question 11

When we describe a population of nominal data, with exactly two categories, the multinomial experiment is actually a binomial experiment with one of the categorical outcomes labeled "success" and the other labeled "failure".

Accepted Answer

This statement is true. The multinomial experiment refers to the scenario where we are observing the frequency of occurrence of different categories in a population, and if there are only two categories, it becomes a binomial experiment with one category considered as "success" and the other considered as "failure".

Question 12

Suppose that two shipping companies, A and B, each decide to estimate the annual percentage of shipments on which a $100 or greater claim for loss or damage was filed by sampling their records, and they report the data shown below. $$\begin{array} { | l | c c | } \hline & \text { Company A } & \text { Company B } \ \hline \text { Total shipments sampled } & \text { 800 } & \text { 600 } \ \text { Number of shipments with a claim } \geq \$ 100 & 200 & 100 \ \hline \end{array}$$ The owner of Company B is hoping to use these data to show that her company is superior to Company A with regard to the percentage of claims filed. Which test would be used to properly analyze the data in this experiment? A)The $\chi$² test of a contingency table in a two-way contingency table. B)The $\chi$² goodness-of-fitness test. C)The z-test for the difference in two proportions. D)The ANOVA F test for main treatment effect.

Accepted Answer

The z-test for the difference in two proportions is used to compare the proportions of two independent samples. In this case, we are comparing the proportion of shipments with a claim of $100 or greater for Company A and Company B.

Question 13

If we use the chi-squared method of analysis we must first check that there are at least 5 observations in each cell of the contingency table.

Accepted Answer

The answer of If we use the chi-squared method of...

Question 14

To describe a population with more than two categories you can only use a chi-squared goodness-of-fit test.

Accepted Answer

The answer of To describe a population with more than...

Question 15

Mathematical statisticians have established that if we square the value of z, the test statistic for the test of one proportion p, we produce the $\chi$² statistic. That is, z² = $\chi$².

Accepted Answer

This statement is true. Squaring the z-value for the test of one proportion produces a chi-squared statistic with 1 degree of freedom, which is equivalent to an F(1,1) distribution.

Question 16

A test for the differences between two proportions can be performed using the chi-squared distribution.

Accepted Answer

The chi-squared distribution can be used to test for differences between two proportions when comparing two independent groups.

Question 17

The chi-squared distribution is used in:
A)a goodness-of-fit test.
B)a test of a contingency table.
C)describing a population having more than two categories.
D)All of these choices are true.

Accepted Answer

The chi-squared distribution is used in a goodness-of-fit test, a test of a contingency table, and describing a population having more than two categories. Therefore, all of these choices are true.

Question 18

Which of the following tests does not use the chi-squared distribution?
A)Test of a contingency table.
B)Goodness-of-fit test.
C)One tailed test for two proportions.
D)None of these choices.

Accepted Answer

The one tailed test for two proportions typically uses the z-distribution or the t-distribution, not the chi-squared distribution. A and B both use the chi-squared distribution. D is not the best choice because one of the choices (C) is not a valid answer.

Question 19

In testing the difference between two proportions using the normal distribution, we may use either a one-tailed or two-tailed test.

Accepted Answer

This is true, we can use either a one-tailed or two-tailed test when testing the difference between two proportions using the normal distribution. Choosing between a one-tailed or two-tailed test depends on the direction of the alternative hypothesis and the specific research question being investigated.

Question 20

A test for whether one proportion is higher than the other can be performed using the chi-squared distribution.

Accepted Answer

A test for whether one proportion is higher than the other is typically performed using a two-sample t-test or a z-test. The chi-squared distribution is commonly used to test for independence between categorical variables or for goodness of fit for a distribution.

Quiz 15: Chi-Squared Tests Optional

If we want to conduct a two-tail test of a population proportion, we can employ:

If we want to conduct a one-tail test of a population proportion, we can employ:

The squared difference between the observed and expected frequencies should be large if there is a significant difference between the proportions.

Which of the following tests is used to analyze nominal data?

When we test for differences between two populations of nominal data with two categories, we can use only one technique, namely, the chi-squared test of a contingency table.

Which of the following tests is appropriate for nominal data if the problem objective is to compare two populations and the number of categories exceeds 2?

If we want to perform a one-tail test for differences between two populations of nominal data with exactly two categories, we must employ the z-test of p₁ -p₂.

Which of the following statements is true for chi-squared tests?

Which of the following tests is appropriate for nominal data if the problem objective is to compare two or more populations and the number of categories is at least 2?

If we want to perform a two-tail test for differences between two populations of nominal data with exactly two categories, we can employ either the z-test of p₁ - p₂, or the chi-squared test of a contingency table.

When we describe a population of nominal data, with exactly two categories, the multinomial experiment is actually a binomial experiment with one of the categorical outcomes labeled "success" and the other labeled "failure".

If we use the chi-squared method of analysis we must first check that there are at least 5 observations in each cell of the contingency table.

To describe a population with more than two categories you can only use a chi-squared goodness-of-fit test.

Mathematical statisticians have established that if we square the value of z, the test statistic for the test of one proportion p, we produce the $\chi$ ² statistic. That is, z² = $\chi$ ².

A test for the differences between two proportions can be performed using the chi-squared distribution.

The chi-squared distribution is used in:

Which of the following tests does not use the chi-squared distribution?

In testing the difference between two proportions using the normal distribution, we may use either a one-tailed or two-tailed test.

A test for whether one proportion is higher than the other can be performed using the chi-squared distribution.

Quiz 15: Chi-Squared Tests Optional

If we want to conduct a two-tail test of a population proportion, we can employ:

If we want to conduct a one-tail test of a population proportion, we can employ:

The squared difference between the observed and expected frequencies should be large if there is a significant difference between the proportions.

Which of the following tests is used to analyze nominal data?

When we test for differences between two populations of nominal data with two categories, we can use only one technique, namely, the chi-squared test of a contingency table.

Which of the following tests is appropriate for nominal data if the problem objective is to compare two populations and the number of categories exceeds 2?

If we want to perform a one-tail test for differences between two populations of nominal data with exactly two categories, we must employ the z-test of p1 -p2.

Which of the following statements is true for chi-squared tests?

Which of the following tests is appropriate for nominal data if the problem objective is to compare two or more populations and the number of categories is at least 2?

If we want to perform a two-tail test for differences between two populations of nominal data with exactly two categories, we can employ either the z-test of p1 - p2, or the chi-squared test of a contingency table.

When we describe a population of nominal data, with exactly two categories, the multinomial experiment is actually a binomial experiment with one of the categorical outcomes labeled "success" and the other labeled "failure".

If we use the chi-squared method of analysis we must first check that there are at least 5 observations in each cell of the contingency table.

To describe a population with more than two categories you can only use a chi-squared goodness-of-fit test.

Mathematical statisticians have established that if we square the value of z, the test statistic for the test of one proportion p, we produce the χ\chiχ 2 statistic. That is, z2 = χ\chiχ 2.

A test for the differences between two proportions can be performed using the chi-squared distribution.

The chi-squared distribution is used in:

Which of the following tests does not use the chi-squared distribution?

In testing the difference between two proportions using the normal distribution, we may use either a one-tailed or two-tailed test.

A test for whether one proportion is higher than the other can be performed using the chi-squared distribution.

If we want to perform a one-tail test for differences between two populations of nominal data with exactly two categories, we must employ the z-test of p₁ -p₂.

If we want to perform a two-tail test for differences between two populations of nominal data with exactly two categories, we can employ either the z-test of p₁ - p₂, or the chi-squared test of a contingency table.

Mathematical statisticians have established that if we square the value of z, the test statistic for the test of one proportion p, we produce the $\chi$ ² statistic. That is, z² = $\chi$ ².