Choosing a Test a. You wish to test whether an association exists between a categorical variable (such as rank of a professor at a university. assuming four ranks) and a numerical variable (such as yearly salary). b. You wish to test whether the means of a numerical variable are different for two possible values of a categorical variable (such as yearly salary for gender).

Question

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Answer 1

Textbook Question

Chapter 11, Problem 1SE

Choosing a Test

a. You wish to test whether an association exists between a categorical variable (such as rank of a professor at a university. assuming four ranks) and a numerical variable (such as yearly salary).

b. You wish to test whether the means of a numerical variable are different for two possible values of a categorical variable (such as yearly salary for gender).

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution & Answer

To determine

Determine the appropriate test to test whether there is an association between categorical and numerical variables.

Answer to Problem 1SE

ANOVA test is used to test the association between categorical and numerical variables.

Explanation of Solution

Reasons for correct answer:

ANOVA s a parametric statistical test which is used to test the differences among the group means in a sample or population. In ANOVA test, we assume that the sample is drawn from normally distributed population and the population variance is equal.

In this case, one variable is numerical (yearly salary) and other variable is categorical (4 ranks of a professor). So, there are four groups and ANOVA is the only parametric test which is used to compares the means of more than two populations.

Reasons for incorrect answers:

One-sample t-test is used to test whether the sample mean is significantly different from known or hypothesized value. So, we cannot use this test to compare the mean of more than two populations.

Two-sample t-test is used to test whether the two population mean is equal or not. So, this test is not suitable to compare the means of more than two populations.

Chi square test is a non-parametric statistical test is used to determine the relationship between two categorical variables. Chi-square is not a appropriate test for numerical variable. So, we cannot use a chi square test because one variable (yearly salary) is numerical.

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Answer 2

Textbook Question

Chapter 11, Problem 1SE

Choosing a Test

a. You wish to test whether an association exists between a categorical variable (such as rank of a professor at a university. assuming four ranks) and a numerical variable (such as yearly salary).

b. You wish to test whether the means of a numerical variable are different for two possible values of a categorical variable (such as yearly salary for gender).

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution & Answer

To determine

Determine the appropriate test to test whether there is an association between categorical and numerical variables.

Answer to Problem 1SE

ANOVA test is used to test the association between categorical and numerical variables.

Explanation of Solution

Reasons for correct answer:

ANOVA s a parametric statistical test which is used to test the differences among the group means in a sample or population. In ANOVA test, we assume that the sample is drawn from normally distributed population and the population variance is equal.

In this case, one variable is numerical (yearly salary) and other variable is categorical (4 ranks of a professor). So, there are four groups and ANOVA is the only parametric test which is used to compares the means of more than two populations.

Reasons for incorrect answers:

One-sample t-test is used to test whether the sample mean is significantly different from known or hypothesized value. So, we cannot use this test to compare the mean of more than two populations.

Two-sample t-test is used to test whether the two population mean is equal or not. So, this test is not suitable to compare the means of more than two populations.

Chi square test is a non-parametric statistical test is used to determine the relationship between two categorical variables. Chi-square is not a appropriate test for numerical variable. So, we cannot use a chi square test because one variable (yearly salary) is numerical.

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Answer 3

Textbook Question

Chapter 11, Problem 1SE

Choosing a Test

a. You wish to test whether an association exists between a categorical variable (such as rank of a professor at a university. assuming four ranks) and a numerical variable (such as yearly salary).

b. You wish to test whether the means of a numerical variable are different for two possible values of a categorical variable (such as yearly salary for gender).

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution & Answer

To determine

Determine the appropriate test to test whether there is an association between categorical and numerical variables.

Answer to Problem 1SE

ANOVA test is used to test the association between categorical and numerical variables.

Explanation of Solution

Reasons for correct answer:

ANOVA s a parametric statistical test which is used to test the differences among the group means in a sample or population. In ANOVA test, we assume that the sample is drawn from normally distributed population and the population variance is equal.

In this case, one variable is numerical (yearly salary) and other variable is categorical (4 ranks of a professor). So, there are four groups and ANOVA is the only parametric test which is used to compares the means of more than two populations.

Reasons for incorrect answers:

One-sample t-test is used to test whether the sample mean is significantly different from known or hypothesized value. So, we cannot use this test to compare the mean of more than two populations.

Two-sample t-test is used to test whether the two population mean is equal or not. So, this test is not suitable to compare the means of more than two populations.

Chi square test is a non-parametric statistical test is used to determine the relationship between two categorical variables. Chi-square is not a appropriate test for numerical variable. So, we cannot use a chi square test because one variable (yearly salary) is numerical.

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Answer 4

Textbook Question

Chapter 11, Problem 1SE

Choosing a Test

a. You wish to test whether an association exists between a categorical variable (such as rank of a professor at a university. assuming four ranks) and a numerical variable (such as yearly salary).

b. You wish to test whether the means of a numerical variable are different for two possible values of a categorical variable (such as yearly salary for gender).

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution & Answer

To determine

Determine the appropriate test to test whether there is an association between categorical and numerical variables.

Answer to Problem 1SE

ANOVA test is used to test the association between categorical and numerical variables.

Explanation of Solution

Reasons for correct answer:

ANOVA s a parametric statistical test which is used to test the differences among the group means in a sample or population. In ANOVA test, we assume that the sample is drawn from normally distributed population and the population variance is equal.

In this case, one variable is numerical (yearly salary) and other variable is categorical (4 ranks of a professor). So, there are four groups and ANOVA is the only parametric test which is used to compares the means of more than two populations.

Reasons for incorrect answers:

One-sample t-test is used to test whether the sample mean is significantly different from known or hypothesized value. So, we cannot use this test to compare the mean of more than two populations.

Two-sample t-test is used to test whether the two population mean is equal or not. So, this test is not suitable to compare the means of more than two populations.

Chi square test is a non-parametric statistical test is used to determine the relationship between two categorical variables. Chi-square is not a appropriate test for numerical variable. So, we cannot use a chi square test because one variable (yearly salary) is numerical.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

Determine the appropriate test to test whether there is an association between categorical and numerical variables.

Answer to Problem 1SE

ANOVA test is used to test the association between categorical and numerical variables.

Explanation of Solution

Reasons for correct answer:

ANOVA s a parametric statistical test which is used to test the differences among the group means in a sample or population. In ANOVA test, we assume that the sample is drawn from normally distributed population and the population variance is equal.

In this case, one variable is numerical (yearly salary) and other variable is categorical (4 ranks of a professor). So, there are four groups and ANOVA is the only parametric test which is used to compares the means of more than two populations.

Reasons for incorrect answers:

One-sample t-test is used to test whether the sample mean is significantly different from known or hypothesized value. So, we cannot use this test to compare the mean of more than two populations.

Two-sample t-test is used to test whether the two population mean is equal or not. So, this test is not suitable to compare the means of more than two populations.

Chi square test is a non-parametric statistical test is used to determine the relationship between two categorical variables. Chi-square is not a appropriate test for numerical variable. So, we cannot use a chi square test because one variable (yearly salary) is numerical.

Answer 8

Expert Solution & Answer

To determine

Determine the appropriate test to test whether there is an association between categorical and numerical variables.

Answer to Problem 1SE

ANOVA test is used to test the association between categorical and numerical variables.

Explanation of Solution

Reasons for correct answer:

ANOVA s a parametric statistical test which is used to test the differences among the group means in a sample or population. In ANOVA test, we assume that the sample is drawn from normally distributed population and the population variance is equal.

In this case, one variable is numerical (yearly salary) and other variable is categorical (4 ranks of a professor). So, there are four groups and ANOVA is the only parametric test which is used to compares the means of more than two populations.

Reasons for incorrect answers:

One-sample t-test is used to test whether the sample mean is significantly different from known or hypothesized value. So, we cannot use this test to compare the mean of more than two populations.

Two-sample t-test is used to test whether the two population mean is equal or not. So, this test is not suitable to compare the means of more than two populations.

Chi square test is a non-parametric statistical test is used to determine the relationship between two categorical variables. Chi-square is not a appropriate test for numerical variable. So, we cannot use a chi square test because one variable (yearly salary) is numerical.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

Determine the appropriate test to test whether there is an association between categorical and numerical variables.

Answer 12

Answer to Problem 1SE

ANOVA test is used to test the association between categorical and numerical variables.

Answer 13

Explanation of Solution

Reasons for correct answer:

ANOVA s a parametric statistical test which is used to test the differences among the group means in a sample or population. In ANOVA test, we assume that the sample is drawn from normally distributed population and the population variance is equal.

In this case, one variable is numerical (yearly salary) and other variable is categorical (4 ranks of a professor). So, there are four groups and ANOVA is the only parametric test which is used to compares the means of more than two populations.

Reasons for incorrect answers:

One-sample t-test is used to test whether the sample mean is significantly different from known or hypothesized value. So, we cannot use this test to compare the mean of more than two populations.

Two-sample t-test is used to test whether the two population mean is equal or not. So, this test is not suitable to compare the means of more than two populations.

Chi square test is a non-parametric statistical test is used to determine the relationship between two categorical variables. Chi-square is not a appropriate test for numerical variable. So, we cannot use a chi square test because one variable (yearly salary) is numerical.

Answer 14

Ch. 11 - Choosing a Test a. You wish to test whether an...Ch. 11 - Prob. 2SE Ch. 11 - Bonferroni Correction (Example 1) Suppose you have...Ch. 11 - Prob. 4SE Ch. 11 - Prob. 5SE Ch. 11 - Prob. 6SE Ch. 11 - Prob. 7SE Ch. 11 - Prob. 8SE Ch. 11 - Prob. 9SE Ch. 11 - Prob. 10SE

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