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Inferential Statistics

Description: This quiz covers the fundamental concepts and techniques of inferential statistics, including hypothesis testing, confidence intervals, and regression analysis.
Number of Questions: 15
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Tags: inferential statistics hypothesis testing confidence intervals regression analysis
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In hypothesis testing, what is the probability of rejecting the null hypothesis when it is actually true?

  1. Type I error

  2. Type II error

  3. Significance level

  4. Critical value

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Correct Option: A
Explanation:

Type I error is the probability of rejecting the null hypothesis when it is actually true. It is also known as the false positive rate.

What is the probability of failing to reject the null hypothesis when it is actually false?

  1. Type I error

  2. Type II error

  3. Significance level

  4. Critical value

Show answer
Correct Option: B
Explanation:

Type II error is the probability of failing to reject the null hypothesis when it is actually false. It is also known as the false negative rate.

The significance level of a hypothesis test is the probability of:

  1. Rejecting the null hypothesis when it is true

  2. Failing to reject the null hypothesis when it is false

  3. Making a correct decision

  4. Making an incorrect decision

Show answer
Correct Option: A
Explanation:

The significance level is the probability of rejecting the null hypothesis when it is actually true. It is typically set at 0.05 or 0.01.

The critical value of a hypothesis test is the:

  1. Value of the test statistic that separates the rejection region from the non-rejection region

  2. Value of the test statistic that is equal to the significance level

  3. Value of the test statistic that is equal to the p-value

  4. Value of the test statistic that is equal to the null hypothesis

Show answer
Correct Option: A
Explanation:

The critical value is the value of the test statistic that separates the rejection region from the non-rejection region. It is determined by the significance level and the distribution of the test statistic.

In a confidence interval, the confidence level is the:

  1. Probability that the interval contains the true population parameter

  2. Probability that the interval does not contain the true population parameter

  3. Probability that the sample mean is equal to the true population parameter

  4. Probability that the sample proportion is equal to the true population proportion

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Correct Option: A
Explanation:

The confidence level is the probability that the confidence interval contains the true population parameter. It is typically set at 95% or 99%.

The margin of error of a confidence interval is:

  1. Half the width of the interval

  2. The difference between the upper and lower bounds of the interval

  3. The amount by which the sample mean is likely to differ from the true population mean

  4. The amount by which the sample proportion is likely to differ from the true population proportion

Show answer
Correct Option: A
Explanation:

The margin of error is half the width of the confidence interval. It is the amount by which the sample mean or proportion is likely to differ from the true population mean or proportion.

In regression analysis, the dependent variable is the:

  1. Variable that is being predicted

  2. Variable that is used to predict the other variable

  3. Variable that is constant

  4. Variable that is random

Show answer
Correct Option: A
Explanation:

The dependent variable is the variable that is being predicted. It is the variable that is affected by the independent variable.

In regression analysis, the independent variable is the:

  1. Variable that is being predicted

  2. Variable that is used to predict the other variable

  3. Variable that is constant

  4. Variable that is random

Show answer
Correct Option: B
Explanation:

The independent variable is the variable that is used to predict the other variable. It is the variable that causes the dependent variable to change.

The coefficient of determination (R-squared) in regression analysis is a measure of:

  1. The strength of the relationship between the independent and dependent variables

  2. The amount of variation in the dependent variable that is explained by the independent variable

  3. The proportion of the variance in the dependent variable that is accounted for by the independent variable

  4. All of the above

Show answer
Correct Option: D
Explanation:

The coefficient of determination (R-squared) is a measure of the strength of the relationship between the independent and dependent variables, the amount of variation in the dependent variable that is explained by the independent variable, and the proportion of the variance in the dependent variable that is accounted for by the independent variable.

The slope of the regression line in regression analysis is a measure of:

  1. The change in the dependent variable for a one-unit change in the independent variable

  2. The average change in the dependent variable for a one-unit change in the independent variable

  3. The rate of change of the dependent variable with respect to the independent variable

  4. All of the above

Show answer
Correct Option: D
Explanation:

The slope of the regression line is a measure of the change in the dependent variable for a one-unit change in the independent variable, the average change in the dependent variable for a one-unit change in the independent variable, and the rate of change of the dependent variable with respect to the independent variable.

In ANOVA, the F-statistic is a measure of:

  1. The ratio of the variance between groups to the variance within groups

  2. The ratio of the mean square between groups to the mean square within groups

  3. The ratio of the sum of squares between groups to the sum of squares within groups

  4. All of the above

Show answer
Correct Option: D
Explanation:

The F-statistic in ANOVA is a measure of the ratio of the variance between groups to the variance within groups, the ratio of the mean square between groups to the mean square within groups, and the ratio of the sum of squares between groups to the sum of squares within groups.

In ANOVA, the p-value is a measure of:

  1. The probability of obtaining a test statistic as extreme as or more extreme than the observed test statistic, assuming the null hypothesis is true

  2. The probability of rejecting the null hypothesis when it is actually true

  3. The probability of failing to reject the null hypothesis when it is actually false

  4. All of the above

Show answer
Correct Option: A
Explanation:

The p-value in ANOVA is a measure of the probability of obtaining a test statistic as extreme as or more extreme than the observed test statistic, assuming the null hypothesis is true.

In ANOVA, the null hypothesis is that:

  1. The means of all groups are equal

  2. The variances of all groups are equal

  3. The distributions of all groups are normal

  4. All of the above

Show answer
Correct Option: A
Explanation:

The null hypothesis in ANOVA is that the means of all groups are equal.

In ANOVA, the alternative hypothesis is that:

  1. The means of at least two groups are different

  2. The variances of at least two groups are different

  3. The distributions of at least two groups are not normal

  4. All of the above

Show answer
Correct Option: A
Explanation:

The alternative hypothesis in ANOVA is that the means of at least two groups are different.

In ANOVA, the degrees of freedom for the between-groups variance is:

  1. k - 1

  2. n - k

  3. k(n - 1)

  4. n(k - 1)

Show answer
Correct Option: A
Explanation:

The degrees of freedom for the between-groups variance is k - 1, where k is the number of groups.

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