Master Inferential Statistics: Hypothesis Testing, Confidence Intervals, and Regression Analysis

Question 1

In hypothesis testing, what's the difference between a Type I error and a Type II error?

Accepted Answer

Type I error: rejecting the null hypothesis when it's true; Type II error: accepting the null hypothesis when it's false

Answer

Type I error: accepting the null hypothesis when it's false; Type II error: rejecting the null hypothesis when it's true

Answer

Both errors occur when the null hypothesis is false

Answer

Both errors occur when the null hypothesis is true

Question 2

Given a 95% confidence interval for the mean weight of newborn babies as (6.2 pounds, 7.0 pounds), which statement accurately describes the true mean weight of newborn babies?

Accepted Answer

It falls within the range of 6.2 pounds to 7.0 pounds

Answer

It is precisely 6.6 pounds

Answer

It lies outside the interval (6.2 pounds, 7.0 pounds)

Question 3

What type of error occurs when we reject a true null hypothesis?

Accepted Answer

Type I error (False positive)

Answer

Type II error (False negative)

Answer

Alpha error

Answer

Beta error

Question 4

How does increasing the sample size affect the width of a confidence interval?

Accepted Answer

The confidence interval narrows.

Answer

The confidence interval widens.

Answer

The confidence interval remains unchanged.

Answer

The relationship is non-linear.

Question 5

Which of the following is NOT an assumption of linear regression?

Accepted Answer

Autocorrelation among residuals

Answer

Linear relationship between variables

Answer

Normally distributed residuals

Answer

Homoscedasticity of residuals

Question 6

What does the slope of a regression line represent?

Accepted Answer

Average change in the dependent variable per unit change in the independent variable

Answer

Value of the dependent variable when the independent variable is zero

Answer

Difference between observed and predicted values of the dependent variable

Answer

Sum of squared residuals

Question 7

What is the function of the coefficient of determination?

Accepted Answer

Measure strength and direction of linear relationship

Answer

Predict value of dependent variable for given independent variable

Answer

Determine significance of regression model

Answer

Calculate confidence interval for regression slope

Question 8

What is the key distinction between a p-value and a confidence interval?

Accepted Answer

P-value is a probability, confidence interval is a range of values

Answer

P-value is a range of values, confidence interval is a probability

Answer

They are equivalent concepts

Answer

P-value is always less than or equal to a confidence interval

Question 9

In hypothesis testing, the probability of falsely rejecting the null hypothesis when it is true is known as the:

Accepted Answer

Type I error

Answer

Alpha error

Answer

Beta error

Answer

Type II error

Question 10

A 95% confidence interval for a population mean indicates that:

Accepted Answer

There is a 95% chance that the true population mean lies within the interval

Answer

The sample mean is within the interval 95% of the time

Answer

The probability of obtaining a sample mean that falls outside the interval is 5%

Answer

95% of the data points in the population fall within the interval

Question 11

Which statistical test is used to determine if there is a significant difference between the means of two independent populations?

Accepted Answer

t-test

Answer

ANOVA

Answer

Chi-square test

Answer

Correlation coefficient

Question 12

Which measure indicates the strength and direction of the linear relationship between two variables?

Accepted Answer

Correlation coefficient

Answer

Regression coefficient

Answer

Slope

Answer

Y-intercept

Question 13

In a chi-square test for independence, the expected frequency for a particular cell is calculated by:

Accepted Answer

Multiplying the row and column totals and dividing by the sample size

Answer

Summing the row and column totals and dividing by 2

Answer

Summing the row and column totals and multiplying by the sample size

Answer

Squaring the row total and subtracting the column total

Question 14

What's the main purpose of conducting a power analysis before hypothesis testing?

Accepted Answer

Determine the minimum sample size for a meaningful effect

Answer

Calculate the probability of rejecting the null hypothesis

Answer

Predict the effect's magnitude

Answer

Guarantee statistically significant findings

Question 15

In a two-sample t-test, the null hypothesis states that:

Accepted Answer

The means of the two populations are equal.

Answer

The means of the two populations are not equal.

Answer

The variances of the two populations are equal.

Answer

The variances of the two populations are not equal.

Question 16

A confidence interval with a margin of error of 0.05 has a confidence level of:

Accepted Answer

95%

Answer

50%

Answer

75%

Answer

90%

Question 17

The primary purpose of a confidence interval is:

Accepted Answer

To estimate the population mean with a known margin of error.

Answer

To test the significance of a difference between means.

Answer

To predict future values of a variable.

Answer

To determine the relationship between two variables.

Question 18

A negative correlation coefficient indicates that:

Accepted Answer

Variables are negatively correlated.

Answer

Variables are positively correlated.

Answer

No relationship exists between variables.

Answer

Relationship between variables is curvilinear.

Question 19

A population differs from a sample in that a population is:

Accepted Answer

The entire group being studied.

Answer

A subset of the group being studied.

Answer

A group with similar characteristics.

Answer

A group randomly selected from another group.

Question 20

In inferential statistics, what is the primary role of degrees of freedom?

Accepted Answer

Define the shape and probability distribution of the test statistic.

Answer

Calculate the sample size required for a given significance level.

Answer

Degrees of freedom are not applicable in inferential statistics.

Answer

Determine the confidence level for a given hypothesis test.

Question 21

In hypothesis testing, what is a Type II error?

Accepted Answer

Failing to reject the null hypothesis when it is false

Answer

Rejecting the null hypothesis when it is true

Answer

Accepting the alternative hypothesis when it is false

Answer

Rejecting the alternative hypothesis when it is true

Question 22

In hypothesis testing, the sampling distribution of sample means primarily helps determine:

Accepted Answer

The likelihood of getting the observed sample mean if the null hypothesis is true

Answer

The precise value of the population mean

Answer

If the sample accurately represents the population

Question 23

A researcher finds a correlation coefficient of -0.75 between two variables. What does this indicate?

Accepted Answer

A strong negative relationship

Answer

A strong positive relationship

Answer

A weak negative relationship

Answer

No relationship

Question 24

Which is an advantage of inferential statistics?

Accepted Answer

It allows us to make inferences about a population based on a sample

Answer

It helps us to identify relationships between variables

Answer

It reduces the amount of data we need to collect

Answer

It eliminates the need for randomization

Question 25

What is the null hypothesis in a hypothesis test?

Accepted Answer

The hypothesis that states that there is no difference between the groups being compared

Answer

The hypothesis that the researcher wants to prove

Answer

The hypothesis that the researcher wants to disprove

Answer

The hypothesis that states that there is a difference between the groups being compared

Question 26

Which of the following is a non-parametric test?

Accepted Answer

Chi-square test

Answer

T-test

Answer

ANOVA

Answer

F-test

Question 27

What could happen to the results of a t-test or ANOVA if the test's assumptions are not met?

Accepted Answer

The results might be misleading.

Answer

The results will always be wrong.

Answer

The p-value will always be wrong.

Answer

The results will have no meaning.

Question 28

Which assumption is essential for the validity of inferential statistical methods?

Accepted Answer

The sample accurately represents the population.

Answer

The data follows a normal distribution.

Answer

The sample size is sufficiently large.

Answer

The data contains no outliers or extreme values.

Question 29

What is the main goal of inferential statistics?

Accepted Answer

To make inferences about a population from sample data.

Answer

To describe a population accurately using sample data.

Answer

To predict future outcomes based on past data.

Answer

To test hypotheses about population parameters.

Question 30

Which of the following is **not** a type of inferential statistics?

Accepted Answer

Descriptive statistics

Answer

Confidence intervals

Answer

Regression analysis

Answer

Hypothesis testing

Question 31

A researcher wants to test the hypothesis that the mean height of all college students is **greater than** 68 inches. Which type of hypothesis test should the researcher use?

Accepted Answer

One-sided right-tailed test

Answer

Chi-square test

Answer

One-sided left-tailed test

Answer

Two-sided test

Question 32

A sample of 100 students has a mean height of 69 inches and a standard deviation of 3 inches. What is the **95% confidence interval** for the mean height of all college students?

Accepted Answer

68.64 to 69.36 inches

Answer

68.42 to 69.58 inches

Answer

68.84 to 69.16 inches

Answer

67.92 to 70.08 inches

Question 33

Which of the following conditions must be met in order to conduct a valid regression analysis?

Accepted Answer

Linear relationship, homoscedasticity, normally distributed residuals

Answer

Nonlinear relationship, heteroscedasticity, normally distributed residuals

Answer

Linear relationship, heteroscedasticity, non-normally distributed residuals

Question 34

A researcher is interested in predicting the final grades of students based on their midterm exam scores. Which of the following is the most appropriate regression model to use?

Accepted Answer

Simple linear regression

Answer

Logistic regression

Answer

Poisson regression

Answer

Multiple regression

Question 35

Which of the following is a measure of effect size in regression analysis?

Accepted Answer

R-squared

Answer

T-statistic

Answer

P-value

Answer

F-statistic

Question 36

When conducting a chi-square test of independence, which of the following conditions must be met?

Accepted Answer

The expected frequencies should be greater than 5 in at least 80% of the cells

Answer

The expected frequencies should be greater than 10 in at least 50% of the cells

Answer

The observed frequencies should be greater than 5 in at least 80% of the cells

Question 37

A researcher is interested in determining if there is a difference in the mean heights of males and females. Which of the following is the most appropriate statistical test to use?

Accepted Answer

Two-sample t-test

Answer

One-sample t-test

Answer

ANOVA

Answer

Chi-square test

Question 38

In hypothesis testing, what is the null hypothesis?

Accepted Answer

The hypothesis stating that there is no significant difference between the groups being compared

Answer

The hypothesis stating that there is a significant difference between the groups being compared

Question 39

What is the primary purpose of a confidence interval?

Accepted Answer

To estimate the true population parameter with a specified level of confidence

Answer

To predict the value of a future observation

Answer

To determine if there is a significant difference between groups

Question 40

What does a p-value represent?

Accepted Answer

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

Answer

The probability of rejecting the null hypothesis

Question 41

Define the difference between a population and a sample:

Accepted Answer

A population encompasses all individuals or objects under study, whereas a sample is a subset drawn from the population

Answer

A population is always larger than a sample

Question 42

Which statistical test is appropriate for comparing the means of two independent groups?

Accepted Answer

Two-sample t-test

Answer

Chi-square test

Answer

Analysis of variance

Answer

One-sample t-test

Question 43

Explain the central limit theorem:

Accepted Answer

As sample size increases, the distribution of sample means approaches a normal distribution, regardless of the shape of the population distribution

Answer

The mean of the sample always equals the mean of the population

Question 44

Identify a potential source of sampling bias:

Accepted Answer

Non-response

Answer

Sampling error

Answer

Outliers

Answer

Measurement error

Question 45

Which of the following is NOT a step in hypothesis testing?

Accepted Answer

Collect data

Answer

Interpret the results

Answer

Analyze the data

Answer

Formulate a hypothesis

Question 46

Which of the following is a type of regression analysis?

Accepted Answer

Simple linear regression

Answer

Cluster analysis

Answer

Logistic regression

Answer

Time series analysis

Question 47

The null hypothesis in a hypothesis test is:

Accepted Answer

A statement that there is no difference between the groups

Answer

A statement that the sample mean is equal to the population mean

Answer

A statement that there is a difference between the groups

Question 48

The p-value in a hypothesis test is:

Accepted Answer

The probability of obtaining the observed results, assuming the null hypothesis is true

Answer

The probability of rejecting the null hypothesis

Answer

The probability of making a Type I error

Question 49

Which of the following is a statistical test that is used to compare the means of two independent groups?

Accepted Answer

Two-sample t-test

Answer

One-sample t-test

Answer

Chi-square test

Answer

ANOVA