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Statistical Inference

Description: This quiz covers the fundamental concepts and techniques of statistical inference, including hypothesis testing, confidence intervals, and regression analysis.
Number of Questions: 15
Created by:
Tags: statistical inference hypothesis testing confidence intervals regression analysis
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In hypothesis testing, the null hypothesis is:

  1. The hypothesis that is being tested

  2. The hypothesis that is assumed to be true

  3. The hypothesis that is rejected if the test statistic is significant

  4. The hypothesis that is accepted if the test statistic is not significant

Show answer
Correct Option: B
Explanation:

The null hypothesis is the hypothesis that is assumed to be true before the data is collected. It is the hypothesis that is being tested.

The alternative hypothesis is:

  1. The hypothesis that is being tested

  2. The hypothesis that is assumed to be true

  3. The hypothesis that is rejected if the test statistic is significant

  4. The hypothesis that is accepted if the test statistic is not significant

Show answer
Correct Option: A
Explanation:

The alternative hypothesis is the hypothesis that is being tested. It is the hypothesis that is being compared to the null hypothesis.

The test statistic is:

  1. A measure of the difference between the observed data and the expected data

  2. A measure of the probability of obtaining the observed data

  3. A measure of the significance of the observed data

  4. A measure of the power of the test

Show answer
Correct Option: A
Explanation:

The test statistic is a measure of the difference between the observed data and the expected data. It is used to determine whether the observed data is significantly different from the expected data.

The p-value is:

  1. The probability of obtaining the observed data, assuming the null hypothesis is true

  2. The probability of obtaining the observed data, assuming the alternative hypothesis is true

  3. The probability of rejecting the null hypothesis, assuming the null hypothesis is true

  4. The probability of rejecting the null hypothesis, assuming the alternative hypothesis is true

Show answer
Correct Option: A
Explanation:

The p-value is the probability of obtaining the observed data, assuming the null hypothesis is true. It is used to determine whether the observed data is significantly different from the expected data.

A confidence interval is:

  1. A range of values within which the true population parameter is likely to fall

  2. A range of values within which the sample statistic is likely to fall

  3. A range of values within which the test statistic is likely to fall

  4. A range of values within which the p-value is likely to fall

Show answer
Correct Option: A
Explanation:

A confidence interval is a range of values within which the true population parameter is likely to fall. It is constructed using the sample statistic and the standard error of the sample statistic.

The level of significance is:

  1. The probability of rejecting the null hypothesis, assuming the null hypothesis is true

  2. The probability of rejecting the null hypothesis, assuming the alternative hypothesis is true

  3. The probability of accepting the null hypothesis, assuming the null hypothesis is true

  4. The probability of accepting the null hypothesis, assuming the alternative hypothesis is true

Show answer
Correct Option: A
Explanation:

The level of significance is the probability of rejecting the null hypothesis, assuming the null hypothesis is true. It is typically set at 0.05 or 0.01.

The power of a test is:

  1. The probability of rejecting the null hypothesis, assuming the null hypothesis is true

  2. The probability of rejecting the null hypothesis, assuming the alternative hypothesis is true

  3. The probability of accepting the null hypothesis, assuming the null hypothesis is true

  4. The probability of accepting the null hypothesis, assuming the alternative hypothesis is true

Show answer
Correct Option: B
Explanation:

The power of a test is the probability of rejecting the null hypothesis, assuming the alternative hypothesis is true. It is typically calculated using the non-central t-distribution.

In regression analysis, the dependent variable is:

  1. The variable that is being predicted

  2. The variable that is being used to predict the dependent variable

  3. The variable that is being controlled for

  4. The variable that is being measured

Show answer
Correct Option: A
Explanation:

In regression analysis, the dependent variable is the variable that is being predicted. It is the variable that is being modeled as a function of the independent variables.

In regression analysis, the independent variable is:

  1. The variable that is being predicted

  2. The variable that is being used to predict the dependent variable

  3. The variable that is being controlled for

  4. The variable that is being measured

Show answer
Correct Option: B
Explanation:

In regression analysis, the independent variable is the variable that is being used to predict the dependent variable. It is the variable that is being used to model the dependent variable.

In regression analysis, the coefficient of determination is:

  1. The proportion of the variance in the dependent variable that is explained by the independent variables

  2. The proportion of the variance in the dependent variable that is not explained by the independent variables

  3. The proportion of the variance in the independent variables that is explained by the dependent variable

  4. The proportion of the variance in the independent variables that is not explained by the dependent variable

Show answer
Correct Option: A
Explanation:

In regression analysis, the coefficient of determination is the proportion of the variance in the dependent variable that is explained by the independent variables. It is a measure of how well the independent variables fit the dependent variable.

In regression analysis, the standard error of the estimate is:

  1. The standard deviation of the residuals

  2. The standard deviation of the dependent variable

  3. The standard deviation of the independent variables

  4. The standard deviation of the coefficient of determination

Show answer
Correct Option: A
Explanation:

In regression analysis, the standard error of the estimate is the standard deviation of the residuals. It is a measure of how much the observed data deviates from the fitted regression line.

In regression analysis, the t-statistic is:

  1. The ratio of the coefficient of determination to the standard error of the estimate

  2. The ratio of the coefficient of determination to the standard deviation of the dependent variable

  3. The ratio of the coefficient of determination to the standard deviation of the independent variables

  4. The ratio of the coefficient of determination to the standard deviation of the residuals

Show answer
Correct Option: A
Explanation:

In regression analysis, the t-statistic is the ratio of the coefficient of determination to the standard error of the estimate. It is used to test the significance of the regression model.

In regression analysis, the F-statistic is:

  1. The ratio of the mean square error to the mean square regression

  2. The ratio of the mean square regression to the mean square error

  3. The ratio of the mean square error to the standard error of the estimate

  4. The ratio of the standard error of the estimate to the mean square error

Show answer
Correct Option: B
Explanation:

In regression analysis, the F-statistic is the ratio of the mean square regression to the mean square error. It is used to test the significance of the regression model.

In regression analysis, the Durbin-Watson statistic is:

  1. A measure of the autocorrelation of the residuals

  2. A measure of the heteroskedasticity of the residuals

  3. A measure of the normality of the residuals

  4. A measure of the independence of the residuals

Show answer
Correct Option: A
Explanation:

In regression analysis, the Durbin-Watson statistic is a measure of the autocorrelation of the residuals. It is used to test for the presence of autocorrelation in the residuals.

In regression analysis, the Breusch-Godfrey test is:

  1. A test for heteroskedasticity

  2. A test for autocorrelation

  3. A test for normality

  4. A test for independence

Show answer
Correct Option: A
Explanation:

In regression analysis, the Breusch-Godfrey test is a test for heteroskedasticity. It is used to test for the presence of heteroskedasticity in the residuals.

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