Statistical Theory and Methods Learning Quizzes | Master of Arts (MA) in Statistics

Question 1

In a statistical hypothesis test, what is the primary purpose of the null hypothesis?

Accepted Answer

To assume no significant difference between observed data and expected outcomes in the absence of an effect or relationship.

Answer

To state that the null hypothesis is always true and the alternative hypothesis is always false.

Answer

To represent the hypothesis that the researcher aims to prove.

Answer

To have no bearing on the outcome of a statistical test.

Question 2

Explain the fundamental differences between statistical theory and statistical methods, and discuss how they are interconnected.

Accepted Answer

Statistical theory provides the theoretical foundation, while statistical methods offer practical tools for data analysis.

Answer

Statistical methods are more important than statistical theory because they can be directly applied to solve problems.

Answer

Statistical theory and methods are completely separate and unrelated.

Answer

Statistical methods can be used to develop new statistical theories.

Question 3

When the population standard deviation is unknown, which statistical method is used to estimate the population mean?

Accepted Answer

t-test

Answer

Z-test

Answer

Chi-square test

Answer

F-test

Question 4

Which of the following is NOT a measure of central tendency?

Accepted Answer

Variance

Answer

Mean

Answer

Median

Answer

Mode

Question 5

Which probability distribution is commonly used to model the distribution of a continuous random variable that is non-negative and has a significant right skew?

Accepted Answer

Weibull distribution

Answer

Poisson distribution

Answer

Binomial distribution

Answer

Normal distribution

Question 6

Which of the following is NOT an advantage of Bayesian inference?

Accepted Answer

Produces results that are sensitive to the choice of prior.

Answer

Incorporates prior knowledge into the analysis.

Answer

Provides a more intuitive interpretation of probabilities.

Answer

Can handle complex models with many parameters.

Question 7

Which assumption is NOT required for linear regression?

Accepted Answer

Normality of response variable

Answer

Linear relationship between variables

Answer

Constant variance of residuals

Answer

Independence of observations

Question 8

Which of the following is NOT a measure of central tendency?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 9

Which of the following is a non-probability sampling method?

Accepted Answer

Convenience sampling

Answer

Simple random sampling

Answer

Systematic sampling

Answer

Stratified sampling

Question 10

In hypothesis testing, what does a p-value represent?

Accepted Answer

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

Answer

The probability that the null hypothesis is true.

Answer

The significance level for the hypothesis test.

Answer

The confidence level for the hypothesis test.

Question 11

Which of the following is an unethical practice in statistical research?

Accepted Answer

Conducting research without informed consent

Answer

Respecting confidentiality and privacy of data

Answer

Ensuring representative and unbiased sampling

Answer

Avoiding selective reporting or manipulation of data

Question 12

Which of the following is NOT a measure of central tendency?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 13

In hypothesis testing, what is the term for the probability of incorrectly rejecting the true null hypothesis?

Accepted Answer

Type I error

Answer

Type II error

Answer

Power

Question 14

In hypothesis testing, what is the definition of a Type I error?

Accepted Answer

Incorrectly rejecting the null hypothesis

Answer

Incorrectly accepting the null hypothesis

Answer

Incorrectly rejecting the alternative hypothesis

Answer

Incorrectly accepting the alternative hypothesis

Question 15

To determine if the means of two independent samples differ, which statistical test is most suitable?

Accepted Answer

Two-sample t-test

Answer

One-sample t-test

Answer

Chi-square test

Answer

ANOVA

Question 16

Which of the following is NOT a component of statistical inference?

Accepted Answer

Collecting and summarizing data

Answer

Making predictions about a population based on sample data

Answer

Testing hypotheses about population parameters

Answer

Determining the probability of observing a particular sample

Question 17

Which of the following is NOT a parameter of a probability distribution?

Accepted Answer

Median

Answer

Mean

Answer

Variance

Answer

Standard deviation

Question 18

Which statement is NOT an ethical consideration in statistical research?

Accepted Answer

Using statistical methods to manipulate or misrepresent data

Answer

Disclosing data sources and methodologies for transparency

Answer

Protecting participant privacy and confidentiality

Answer

Assessing the potential impact of the research on participants and society

Question 19

To estimate unknown population parameters using sample data, which statistical method is most commonly employed?

Accepted Answer

Confidence intervals

Answer

Hypothesis testing

Answer

Sampling distributions

Answer

Correlation analysis

Question 20

Which of the following is a non-probability sampling method?

Accepted Answer

Convenience sampling

Answer

Simple random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Question 21

Which of the following is NOT a fundamental principle of statistical inference?

Accepted Answer

Extending conclusions beyond the available data

Answer

Drawing inferences about a population based on sample data

Answer

Using probability theory to measure uncertainty

Answer

Ensuring random sampling for data collection

Question 22

In hypothesis testing, what is the main purpose of the null hypothesis?

Accepted Answer

To provide a reference point for evaluating the alternative hypothesis.

Answer

To establish the alternative hypothesis as true.

Answer

To predict the outcome of the hypothesis test.

Answer

To determine the appropriate sample size for the test.

Question 23

In hypothesis testing, how does increasing the sample size affect the power of a statistical test?

Accepted Answer

Increases statistical power

Answer

Reduces statistical power

Answer

Has no effect on statistical power

Answer

Only affects the significance level of a test

Question 24

In statistical inference, the purpose of a confidence interval is to:

Accepted Answer

Estimate the range of values within which the population parameter is likely to fall

Answer

Provide an exact estimate of the population parameter

Answer

Test whether the population parameter is significantly different from a specified value

Answer

Determine the sample size needed to achieve a desired level of confidence

Question 25

Which type of regression analysis is used to model the relationship between a continuous dependent variable and one or more independent variables?

Accepted Answer

Linear regression

Answer

Logistic regression

Answer

Poisson regression

Answer

ANOVA

Question 26

In the context of hypothesis testing, a Type I error occurs when:

Accepted Answer

The null hypothesis is incorrectly rejected

Answer

The null hypothesis is correctly rejected

Answer

The alternative hypothesis is correctly accepted

Answer

The alternative hypothesis is incorrectly accepted

Question 27

In Bayesian statistics, the prior probability represents:

Accepted Answer

The probability of observing a particular event before any data is collected

Answer

The probability of a hypothesis being true after all data is collected

Answer

The probability of a parameter taking on a specific value

Answer

The probability of a random variable being less than a specified value

Question 28

In the context of time series analysis, a stationary process is one that:

Accepted Answer

Has a constant mean and variance

Answer

Has a predictable pattern

Answer

Is independent of time

Answer

Is Gaussian distributed

Question 29

Which of the following is **not** regarded as a fundamental concept in statistical theory?

Accepted Answer

Data mining

Answer

Probability

Answer

Statistical inference

Answer

Regression analysis

Question 30

Which of the following is **not** a recognized sampling method?

Accepted Answer

Quota sampling

Answer

Simple random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Question 31

In statistical inference, what is the probability of rejecting the null hypothesis when it is actually true?

Accepted Answer

Type I error

Answer

Type II error

Answer

Confidence level

Answer

Significance level

Question 32

Which type of regression analysis is used to predict a continuous dependent variable using one or more independent variables?

Accepted Answer

Linear regression

Answer

Logistic regression

Answer

Poisson regression

Answer

Multinomial regression

Question 33

Which of the following statistical tests does not assume that the data follows a normal distribution?

Accepted Answer

Mann-Whitney U test

Answer

t-test

Answer

Chi-squared test

Answer

ANOVA

Question 34

Which of the following is NOT a core concept of statistical theory?

Accepted Answer

Interpolation

Answer

Probability theory

Answer

Statistical inference

Answer

Regression analysis

Question 35

Which statistical test is appropriate for comparing the means of two independent groups when the sample sizes are small (less than 30)?

Accepted Answer

Mann-Whitney U test

Answer

t-test

Answer

Pearson's correlation coefficient

Answer

Chi-square test

Question 36

What is the main objective of regression analysis?

Accepted Answer

To predict the dependent variable based on one or more independent variables

Answer

To test the significance of a relationship between variables

Answer

To create a visual representation of data

Answer

To estimate the probability of an event

Question 37

What does the central limit theorem state?

Accepted Answer

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

Answer

The sample mean will always be equal to the population mean

Answer

The variance of a sample will always be less than the variance of the population

Answer

The probability of an event occurring is always 50%

Question 38

Which measure of central tendency is least sensitive to outliers?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 39

In hypothesis testing, what is the null hypothesis typically?

Accepted Answer

The hypothesis that is assumed to be true

Answer

The hypothesis that is being supported

Answer

The hypothesis that is rejected if the test statistic is significant

Answer

The hypothesis that is accepted if the p-value is less than 0.05

Question 40

Which of the following statistical tests is non-parametric?

Accepted Answer

Mann-Whitney U test

Answer

t-test

Answer

Chi-square test

Answer

Analysis of variance (ANOVA)

Question 41

What is the purpose of a p-value in statistical inference?

Accepted Answer

To indicate the probability of obtaining the observed results assuming the null hypothesis is true

Answer

To directly determine whether the null hypothesis should be rejected or not

Answer

To calculate the confidence interval for a population parameter

Answer

To predict the future value of a dependent variable

Question 42

Which of the following is a non-probability sampling method?

Accepted Answer

Convenience sampling

Answer

Simple random sampling

Answer

Systematic sampling

Answer

Stratified sampling

Question 43

The likelihood of an event occurring is determined by:

Accepted Answer

The ratio of favorable outcomes to total possible outcomes

Answer

The ratio of unfavorable outcomes to total possible outcomes

Answer

The difference between favorable and unfavorable outcomes

Answer

The sum of probabilities for all possible outcomes

Question 44

Within hypothesis testing, the null hypothesis is defined as:

Accepted Answer

The hypothesis presumed to be true

Answer

The hypothesis that is subjected to testing

Answer

The hypothesis rejected if the test statistic is significant

Answer

The hypothesis accepted if the test statistic is not significant

Question 45

Which of the following measures variability?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Skewness

Question 46

Which of the following is an example of a discrete random variable?

Accepted Answer

Number of heads in 10 coin flips

Answer

Height of a person

Answer

Average temperature in a city

Answer

Weight of a newborn baby

Question 47

A sample mean is used to approximate which population parameter?

Accepted Answer

Population mean

Answer

Population standard deviation

Answer

Population median

Answer

Population variance

Question 48

What is the primary purpose of using a t-distribution?

Accepted Answer

Hypothesis testing when the sample size is limited

Answer

Hypothesis testing when the sample size is substantial

Answer

Creating confidence intervals for means

Answer

Determining the required sample size

Question 49

What does the coefficient of determination (R-squared) represent?

Accepted Answer

The proportion of variance explained by the model

Answer

The gradient of the regression line

Answer

The intercept of the regression line

Answer

The standard error of the regression

Question 50

What is the primary objective of utilizing a null hypothesis in hypothesis testing?

Accepted Answer

To determine whether there is sufficient evidence to challenge the existing assumption

Answer

To verify that the alternative hypothesis is accurate

Answer

To validate the research methodology

Answer

To calculate the p-value

Question 51

Explain the distinction between population and sample in statistics.

Accepted Answer

The population encompasses the entire group, while the sample is a subset representing the population

Answer

The population refers to the size of the sample, while the sample pertains to the number of measurements

Answer

The population represents the average value, while the sample represents the range of values

Answer

The population represents the median value, while the sample represents the standard deviation

Question 52

In hypothesis testing, what is the probability of rejecting the null hypothesis when it is true?

Accepted Answer

Type I error

Answer

Type II error

Answer

p-value

Answer

Critical value

Question 53

Which of the following is **not** a fundamental concept of probability theory?

Accepted Answer

Maximum likelihood estimation

Answer

Random variable

Answer

Distribution function

Answer

Conditional probability

Question 54

In hypothesis testing, what is the probability of rejecting the null hypothesis when it is **true**?

Accepted Answer

Type I error

Answer

Type II error

Answer

Power of the test

Answer

Level of significance

Question 55

Which type of regression analysis models the relationship between a continuous dependent variable and one or more independent variables?

Accepted Answer

Linear regression

Answer

Logistic regression

Answer

Non-parametric regression

Answer

Factor analysis

Question 56

What is the purpose of a confidence interval?

Accepted Answer

To estimate the population mean with a given level of confidence

Answer

To determine whether a difference between two means is statistically significant

Answer

To predict the value of a future observation

Answer

To identify outliers in a data set

Question 57

Which of the following distributions is used to model **proportions**?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Poisson distribution

Answer

Uniform distribution

Question 58

Which of the following is not a fundamental concept in statistical theory and methods?

Accepted Answer

Causal relationships

Answer

Probability distributions

Answer

Hypothesis testing

Answer

Sampling techniques

Question 59

Which of the following is NOT a measure of central tendency?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Question 60

Which probability distribution is best suited for modeling the time interval between occurrences of an event?

Accepted Answer

Exponential distribution

Answer

Uniform distribution

Answer

Binomial distribution

Answer

Normal distribution

Question 61

Which of the following statistical tests is classified as non-parametric?

Accepted Answer

Mann-Whitney U test

Answer

t-test

Answer

Analysis of Variance (ANOVA)

Answer

Pearson's Correlation Coefficient

Question 62

What distinguishes a population parameter from a sample statistic?

Accepted Answer

A population parameter is a fixed value, whereas a sample statistic is an estimate.

Answer

A sample statistic is a fixed value, whereas a population parameter is an estimate.

Answer

They both represent fixed values.

Answer

They both represent estimated values.

Question 63

For a categorical dependent variable, which regression analysis type is appropriate?

Accepted Answer

Logistic regression

Answer

Linear regression

Answer

Poisson regression

Answer

Negative binomial regression

Question 64

In a bag containing 4 red and 2 blue balls, what is the probability of randomly drawing a red ball?

Accepted Answer

2/3

Answer

1/2

Answer

1/3

Answer

1/6