Question 1

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 statement is true. A one-tailed test is used when we have a directional hypothesis, and we want to test whether one proportion is greater than or less than another proportion. A two-tailed test is used when we have a non-directional hypothesis, and we want to test whether the two proportions are significantly different from each other, regardless of the direction of difference.

Question 2

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 can be used in a goodness-of-fit test, a test of a contingency table, and describing a population having more than two categories.

Question 3

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 4

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 z-test of a population proportion and the chi-squared test of a binomial experiment are both appropriate for testing a population proportion.

Question 5

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 is true. The categories can be labeled as "success" and "failure" to analyze the data using a binomial experiment.

Question 6

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 z-test of p₁ - p₂ is used to test for differences between two populations of nominal data with exactly two categories.

Question 7

If we want to perform a one-tail test of a population proportion p,we can employ either the z-test of p,or the chi-squared goodness-of-fit test.

Accepted Answer

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

Question 8

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 9

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 chi-squared goodness-of-fit test is used when comparing one population to an expected distribution and the z-test for proportions is used for comparing two populations with binary outcomes. Therefore, choice C is the best option.

Question 10

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 11

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

Accepted Answer

The chi-squared distribution is commonly used for tests of independence and goodness-of-fit, but it is not appropriate for testing whether one proportion is higher than another. Tests of proportions typically use the z-test, t-test, or a specialized test such as the McNemar test for paired proportions.

Question 12

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

Accepted Answer

A chi-squared test can be used to compare the proportions of two groups.

Question 13

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

One tailed test for two proportions uses the normal distribution, not the chi-squared distribution.

Question 14

If we want to perform a two-tail test of a population proportion p,we can only use the z-test of p.

Accepted Answer

We can also use a chi-square test or a t-test for proportions depending on the specific scenario and assumptions made.

Question 15

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 for testing differences between two populations of nominal data with exactly two categories.

Question 16

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

The given statement is true because the square of the z-statistic for the test of one proportion p is equal to the chi-squared statistic with 1 degree of freedom.

Question 17

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

The z-test of a population proportion can be used for 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 testing population proportions.

Question 18

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

Accepted Answer

The squared difference between the observed and expected frequencies is used to calculate the chi-squared statistic, and a large chi-squared value indicates a significant difference between the observed and expected frequencies.

Question 19

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

All of the statements are true.

Question 20

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. $$\begin{array} { | l | c c | } \hline & \text { Company A } & \text { Company B } \ \hline \text { Total shipments sampled } & \text { 800 } & \text { 600 } \ \text { Number af shipments with a clain } \geq \$ 100 & 200 & 100 \ \hline \end{array}$$ 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 best test to analyze this data would be the z-test for the difference in two proportions. This is because we are comparing the percentages of claims filed by two different companies, which can be considered two proportions. The z-test is appropriate when we have two proportions and we want to determine if they are significantly different from each other. The other options listed are not appropriate for this type of analysis.

Quiz 15: Chi-Squared Tests

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

The chi-squared distribution is used in:

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.

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

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 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 one-tail test of a population proportion p,we can employ either the z-test of p,or the chi-squared goodness-of-fit test.

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

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?

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.

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

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

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

If we want to perform a two-tail test of a population proportion p,we can only use the z-test of p.

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.

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 statements is true for chi-squared tests?

Quiz 15: Chi-Squared Tests

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

The chi-squared distribution is used in:

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.

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

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 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 one-tail test of a population proportion p,we can employ either the z-test of p,or the chi-squared goodness-of-fit test.

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

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?

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.

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

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

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

If we want to perform a two-tail test of a population proportion p,we can only use the z-test of p.

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 χ\chiχ 2 statistic.That is,z2 = χ\chiχ 2.

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 statements is true for chi-squared tests?

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.