Inferential Statistics: Master Hypothesis Testing, Confidence Intervals, and More

Question 1

For a one-sample t-test, the null hypothesis typically states that:

Accepted Answer

The population mean is equal to the hypothesized value.

Answer

The population mean is not equal to the hypothesized value.

Question 2

Which component is NOT included in a confidence interval?

Accepted Answer

Significance test outcome

Answer

Sample mean

Answer

Standard error of the mean

Answer

Confidence level

Question 3

In ANOVA, which test statistic is used to assess differences among group means?

Accepted Answer

F-statistic

Answer

t-statistic

Answer

Chi-square statistic

Answer

R-squared statistic

Question 4

What is the primary purpose of constructing a confidence interval?

Accepted Answer

To provide an estimate of the range of possible values for a population parameter

Answer

To determine whether there is a statistically significant difference between two groups

Answer

To predict the future value of a dependent variable

Answer

To test the validity of a statistical model

Question 5

In an ANOVA test, what is the null hypothesis?

Accepted Answer

There is no statistically significant difference between the means of two or more groups

Answer

There is a statistically significant difference between the means of two or more groups

Answer

The population means are equal

Answer

The population variances are equal

Question 6

Which measure is used to quantify the effect size in ANOVA?

Accepted Answer

eta-squared

Answer

F-statistic

Answer

R-squared

Answer

Cohen's d

Question 7

What is the main purpose of post-hoc tests in ANOVA?

Accepted Answer

To identify specific groups that differ significantly from each other

Answer

To determine the overall significance of the ANOVA test

Answer

To estimate the population mean for each group

Answer

To test the assumptions of ANOVA

Question 8

Which of the following is considered a non-parametric test?

Accepted Answer

Chi-square test

Answer

t-test

Answer

ANOVA

Answer

Regression analysis

Question 9

What is the role of p-values in hypothesis testing?

Accepted Answer

To determine whether the null hypothesis should be rejected or not

Answer

To estimate the effect size

Answer

To calculate the confidence interval

Answer

To test the assumptions of the statistical test

Question 10

In hypothesis testing, the null hypothesis is rejected when:

Accepted Answer

The p-value is less than the significance level.

Answer

The p-value is greater than the significance level.

Answer

The test statistic is greater than the critical value.

Answer

The test statistic is less than the critical value.

Question 11

A 95% confidence interval for the population mean is:

Accepted Answer

A range of values that have a 95% probability of containing the true mean.

Answer

A single value that has a 95% probability of being the true mean.

Answer

A range of values that has a 5% probability of containing the true mean.

Answer

A single value that has a 5% probability of being the true mean.

Question 12

Which type of regression analysis is used when the dependent variable is binary (yes/no)?

Accepted Answer

Logistic regression

Answer

Linear regression

Answer

Polynomial regression

Answer

Multiple regression

Question 13

In ANOVA, the F-test statistic tests:

Accepted Answer

The variability within groups relative to the variability between groups.

Answer

The equality of means between multiple groups.

Answer

The relationship between two variables.

Answer

The significance of the regression model.

Question 14

The standard error of the mean decreases as the:

Accepted Answer

Sample size increases

Answer

Population mean increases

Answer

Population variance decreases

Answer

Significance level increases

Question 15

A confidence interval for a population proportion has a margin of error of 0.05. This means that:

Accepted Answer

We are 95% confident that the true proportion is within 0.05 of the sample proportion.

Answer

We are 90% confident that the sample proportion is within 0.05 of the true proportion.

Answer

We are 99% confident that the true proportion is within 0.025 of the sample proportion.

Answer

We are 95% confident that the sample proportion is within 0.1 of the true proportion.

Question 16

In multiple regression, the coefficient of determination (R-squared) measures:

Accepted Answer

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

Answer

The correlation between the dependent and independent variables.

Answer

The slope of the regression line.

Answer

The intercept of the regression line.

Question 17

Why is a 95% confidence interval wider than a 90% confidence interval for the same sample and statistic?

Accepted Answer

A higher confidence level requires a larger margin of error to encompass a wider range of plausible values for the population parameter.

Answer

The sample size is smaller for a 95% confidence interval, leading to a wider interval.

Answer

The standard deviation of the population is inherently larger for a 95% confidence interval.

Question 18

Which set of assumptions must be met for a regression analysis to produce reliable results?

Accepted Answer

Linearity between variables, independence of observations, normally distributed errors, and homogeneity of variances (homoscedasticity).

Answer

Linearity, independence, normally distributed errors, heteroscedasticity.

Answer

Linearity, dependence, non-normally distributed errors, homoscedasticity.

Question 19

What is the primary purpose of an ANOVA (Analysis of Variance) test?

Accepted Answer

To compare the means of two or more groups to determine if there is a statistically significant difference between them.

Answer

To assess the significance of a single mean value.

Answer

To examine the correlation between two variables.

Answer

To compare the variances of two or more groups.

Question 20

What constitutes a Type I error in hypothesis testing?

Accepted Answer

Rejecting a null hypothesis that is actually true.

Answer

Failing to reject a null hypothesis that is actually true.

Answer

Accepting a null hypothesis that is actually true.

Answer

Accepting a null hypothesis that is actually false.

Question 21

What does the effect size represent in a statistical test?

Accepted Answer

The magnitude or strength of the effect being investigated, indicating how large the observed difference or relationship is.

Answer

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

Answer

The number of observations included in the sample used for the test.

Question 22

What is the primary purpose of a power analysis in research?

Accepted Answer

To determine the minimum sample size required to achieve a desired level of statistical power, which is the probability of detecting a true effect.

Answer

To test the significance of a statistical result obtained from a study.

Answer

To calculate the effect size of a statistical test to quantify the magnitude of the observed effect.

Question 23

What is the ethical responsibility of a researcher when reporting statistical results?

Accepted Answer

To present the results honestly and accurately, avoiding any misleading or biased interpretations.

Answer

To exaggerate the significance of the results to make them seem more impactful than they truly are.

Answer

To withhold results that do not support the researcher's hypothesis or preferred outcome.