Statistics 2 Quizzes: Test Your Knowledge and Skills

Question 1

In a study examining the effectiveness of a new teaching method on student exam scores, why is randomization crucial for ensuring the reliability of the study's findings?

Accepted Answer

Randomization ensures that each participant has an equal chance of being assigned to either the experimental or control group.

Answer

Randomization guarantees a large enough sample size for meaningful conclusions.

Answer

Randomization ensures that the data follows a normal distribution.

Answer

Randomization is unnecessary if the study follows ethical guidelines.

Question 2

Which assumption is NOT required for non-parametric statistical tests, but is for parametric tests?

Accepted Answer

The data is normally distributed.

Answer

The sample size is large.

Answer

The data is quantitative.

Question 3

In the context of statistical analysis, discuss the ethical considerations that arise from the use of big data.

Accepted Answer

Ethical use of big data requires weighing the potential benefits of analysis against potential risks to individuals and society.

Answer

Using big data for statistical analysis does not raise ethical concerns because of its valuable insights.

Answer

Ethical considerations apply only when big data is sensitive or personal.

Answer

Researchers have no obligation to ensure the ethical use of big data.

Question 4

Why is it crucial to control confounding variables in experiments?

Accepted Answer

To isolate the effect of the treatment variable.

Answer

To reduce the sample size needed.

Answer

To comply with ethical guidelines.

Answer

To make data analysis easier.

Question 5

From the following probability distributions: Normal, Uniform, Poisson, and Exponential, which one is a discrete distribution?

Accepted Answer

Poisson

Answer

Normal

Answer

Uniform

Answer

Exponential

Question 6

Which of these methods ensures a representative sample from a population, giving every individual an equal chance of being selected?

Accepted Answer

Simple random sampling

Answer

Cluster sampling

Answer

Convenience sampling

Answer

Quota sampling

Question 7

In hypothesis testing, what does the null hypothesis represent?

Accepted Answer

The assumption that there is no significant difference or effect

Answer

The statement that we are trying to prove

Answer

The alternative hypothesis

Answer

The conclusion of the test

Question 8

In a chi-square goodness-of-fit test, what is the formula for calculating the degrees of freedom when there are 'k' categories?

Accepted Answer

k - 1

Answer

k + 1

Answer

k - 2

Answer

k + 2

Question 9

What is the term for mistakenly rejecting the null hypothesis when it is actually true in hypothesis testing?

Accepted Answer

Type I error

Answer

Type II error

Answer

Power error

Answer

Significance error

Question 10

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

Accepted Answer

Normality of residuals

Answer

Linearity

Answer

Independence

Answer

Homoscedasticity

Question 11

A dataset consists of two variables, X and Y. The correlation coefficient between X and Y is -0.8. Which of the following statements is true?

Accepted Answer

X and Y have a strong negative linear relationship.

Answer

X and Y have a strong positive linear relationship.

Answer

X and Y have a weak positive linear relationship.

Answer

X and Y have a weak negative linear relationship.

Question 12

Which of the following is a method for estimating the variance of a population?

Accepted Answer

Sample variance

Answer

Population variance

Answer

Standard deviation

Answer

Mean

Question 13

A researcher wants to predict the selling price of a house based on its size and number of bedrooms. Which of the following is the most appropriate statistical model for this purpose?

Accepted Answer

Linear regression

Answer

Logistic regression

Answer

ANOVA

Answer

Factor analysis

Question 14

Which of the following is a measure used to describe the central tendency of a dataset?

Accepted Answer

Mean

Answer

Variance

Answer

Skewness

Answer

Standard deviation

Question 15

Which of the following is a statistical hypothesis test that compares the mean of a sample to a known value?

Accepted Answer

One-sample t-test

Answer

Correlation analysis

Answer

Regression analysis

Answer

ANOVA

Question 16

In a hypothesis test, what is the statement that assumes the null hypothesis is true called?

Accepted Answer

Null hypothesis

Answer

Alternative hypothesis

Answer

Research hypothesis

Answer

Statistical hypothesis

Question 17

Which of the following is a linear regression model?

Accepted Answer

y = a + bx

Answer

y = ax^2 + bx + c

Answer

y = e^x

Answer

y = sin(x)

Question 18

What statistical measure represents the proportion of variance in the dependent variable that is explained by the independent variable in a regression model?

Accepted Answer

Coefficient of determination

Answer

Slope of the regression line

Answer

Y-intercept of the regression line

Answer

Standard error of the estimate

Question 19

What is the primary purpose of examining a residual plot in regression analysis?

Accepted Answer

To detect patterns in the residuals

Answer

To verify the normality of the residuals

Answer

To determine the significance of the regression model

Answer

To predict future values of the dependent variable

Question 20

Which of the following is a **required** assumption for a valid t-test?

Accepted Answer

The data is normally distributed

Answer

The variances of the two groups are equal

Answer

The sample size is large enough

Answer

The population standard deviation is known

Question 21

Which of the following is **not** a potential benefit of using a regression model?

Accepted Answer

Making causal inferences

Answer

Predicting future outcomes

Answer

Identifying relationships between variables

Answer

Testing hypotheses

Question 22

The probability of rolling a 6 on a **fair** dice is:

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 23

The expected value of a random variable X with probability mass function p(x) is calculated as:

Accepted Answer

E(X) = Σx * p(x)

Answer

E(X) = Σp(x) / x

Answer

E(X) = p(x) * x

Answer

E(X) = x * p(x)

Question 24

In hypothesis testing, the null hypothesis proposes that the population mean is 50. The sample mean is 48, and the sample standard deviation is 5. What is the resulting p-value?

Accepted Answer

0.0228

Answer

0.0456

Answer

0.9544

Answer

0.9772

Question 25

Which of the following is a measure of central tendency?

Accepted Answer

Mean

Answer

Variance

Answer

Standard deviation

Answer

Skewness

Question 26

In a regression model, the slope coefficient represents:

Accepted Answer

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

Answer

The intercept of the regression line

Answer

The standard deviation of the dependent variable

Answer

The coefficient of determination

Question 27

Which of the following is NOT an advantage of Bayesian statistics over frequentist statistics?

Accepted Answer

Is less computationally complex

Answer

Incorporates prior knowledge

Answer

Provides more accurate predictions

Answer

Allows for nuanced interpretation of results

Question 28

Which of the following is a measure of the spread or dispersion of a sample?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 29

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

Accepted Answer

t-test for independent samples

Answer

t-test for paired samples

Answer

ANOVA

Answer

χ² test

Question 30

In a linear regression model, the coefficient of determination (R-squared) represents the:

Accepted Answer

Proportion of variance in the dependent variable explained by the independent variable

Answer

Slope of the regression line

Answer

Intercept of the regression line

Answer

Correlation between the dependent and independent variables

Question 31

What is the p-value in a statistical test?

Accepted Answer

The likelihood of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true

Answer

The likelihood of rejecting the null hypothesis

Answer

The likelihood of accepting the null hypothesis

Answer

The strength of evidence against the null hypothesis

Question 32

Which condition is NOT required for the validity of the linear regression model?

Accepted Answer

Dependent errors

Answer

Linearity between the response and predictor variables

Answer

Normally distributed residuals

Answer

Constant variance of residuals

Question 33

A population has a mean of 45 and a standard deviation of 5. What is the probability of obtaining a sample mean of at least 50 from a sample of size 100?

Accepted Answer

0.9772

Answer

0.0228

Answer

0.0028

Answer

0.9972

Question 34

When sampling from a normally distributed population, the sampling distribution of the sample mean is:

Accepted Answer

Normal distribution

Answer

Student's t-distribution

Answer

Chi-square distribution

Answer

Binomial distribution

Question 35

Which statistical error occurs when the null hypothesis is rejected when it is actually true?

Accepted Answer

Type I error

Answer

Type II error

Answer

Sampling error

Answer

Measurement error

Question 36

A scatterplot shows a negative correlation between two variables. What does this indicate?

Accepted Answer

As one variable increases, the other variable decreases

Answer

As one variable increases, the other variable also increases

Answer

There is no relationship between the variables

Answer

The relationship between the variables is non-linear

Question 37

Which of the following sampling methods involves dividing the population into groups and then randomly selecting a sample from each group?

Accepted Answer

Stratified sampling

Answer

Simple random sampling

Answer

Cluster sampling

Answer

Quota sampling

Question 38

In a hypothesis test, the null hypothesis is:

Accepted Answer

The hypothesis that is assumed to be true until proven otherwise

Answer

The hypothesis that is supported by the evidence

Answer

The hypothesis that is rejected if the test statistic is significant

Answer

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

Question 39

The coefficient of determination (R^2) in linear regression represents:

Accepted Answer

The proportion of variance in the dependent variable explained by the independent variable(s)

Answer

The slope of the regression line

Answer

The intercept of the regression line

Answer

The standard deviation of the dependent variable

Question 40

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

Accepted Answer

Range

Answer

Mode

Answer

Mean

Answer

Median

Question 41

A random sample of 100 students is taken from a large population. The sample mean height is 170 cm with a standard deviation of 10 cm. What is the 95% confidence interval for the population mean height?

Accepted Answer

(168.5 cm, 171.5 cm)

Answer

(169 cm, 171 cm)

Answer

(171 cm, 173 cm)

Answer

(170 cm, 172 cm)

Question 42

Which of the following is a Type I error?

Accepted Answer

Rejecting a true null hypothesis

Answer

Accepting a true null hypothesis

Answer

Failing to reject a false null hypothesis

Answer

Accepting a false null hypothesis

Question 43

What is the probability of getting a head when flipping a fair coin?

Accepted Answer

0.5

Answer

1

Answer

0.25

Answer

0.75

Question 44

What is the null hypothesis when testing for the difference between two means?

Accepted Answer

The means of the two populations are equal.

Answer

The sample means are equal.

Answer

The means of the two populations are not equal.

Answer

The sample means are not equal.

Question 45

What is the p-value of a test statistic with a z-score of -2.57?

Accepted Answer

0.01

Answer

0.1

Answer

0.25

Answer

0.05

Question 46

A researcher wants to compare the average heights of students from two different schools. Which hypothesis test would be most appropriate?

Accepted Answer

Two-sample t-test

Answer

One-sample t-test

Answer

ANOVA

Answer

Chi-square test

Question 47

A researcher investigates the relationship between the number of hours of sleep and academic performance. Which type of regression analysis is most suitable for this study?

Accepted Answer

Linear Regression

Answer

Time Series Regression

Answer

Multiple Regression

Answer

Logistic Regression

Question 48

A researcher tests the effectiveness of a new drug. The null hypothesis states the drug has no effect, while the alternative hypothesis states it has a positive effect. The study shows a p-value of 0.03. What is the appropriate conclusion?

Accepted Answer

Reject the null hypothesis

Answer

Accept the alternative hypothesis

Answer

There is not enough evidence to conclude that the drug is effective

Answer

Fail to reject the null hypothesis

Question 49

A researcher wants to analyze the relationship between the number of hours worked per week and the level of job satisfaction. Which type of correlation coefficient is most suitable for this analysis?

Accepted Answer

Pearson's correlation coefficient

Answer

Point-biserial correlation coefficient

Answer

Spearman's rank correlation coefficient

Answer

Kendall's tau correlation coefficient

Question 50

A random variable X follows a binomial distribution with n = 10 and p = 0.4. What is the expected value of X?

Accepted Answer

4

Answer

10

Answer

6

Answer

0.4

Question 51

A researcher wants to compare the effectiveness of two teaching methods. They randomly assign students to two groups, one taught using Method A and the other using Method B. What is the most appropriate statistical test to compare the average test scores of the two groups?

Accepted Answer

Independent samples t-test

Answer

Paired samples t-test

Answer

Chi-squared test

Answer

Analysis of variance (ANOVA)

Question 52

The probability of a student passing a driving test on their first attempt is 0.6. If a student has already failed the test once, what is the probability they will pass on their second attempt?

Accepted Answer

0.6

Answer

0.4

Answer

0.24

Answer

0.36

Question 53

A study found a strong positive correlation between ice cream sales and swimming pool attendance. Which of the following statements is the most appropriate interpretation of this finding?

Accepted Answer

Correlation does not imply causation, and there may be a third variable influencing both variables.

Answer

Increased ice cream sales cause increased swimming pool attendance.

Answer

Increased swimming pool attendance causes increased ice cream sales.

Question 54

What is the critical value of the t-statistic for a one-tailed hypothesis test with a significance level of 0.05 and a sample size of 20?

Accepted Answer

1.729

Answer

1.645

Answer

2.33

Answer

1.96

Question 55

Which of the following distributions is most appropriate for modelling the time until an event occurs?

Accepted Answer

Exponential distribution

Answer

Normal distribution

Answer

Poisson distribution

Answer

Binomial distribution

Question 56

In a simple linear regression model, what does the slope of the regression line represent?

Accepted Answer

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

Answer

The mean value of the dependent variable.

Answer

The strength and direction of the correlation.

Question 57

Which of the following is a type II error in hypothesis testing?

Accepted Answer

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

Answer

Rejecting the null hypothesis when it is actually true.

Answer

Accepting the alternative hypothesis when it is actually false.

Question 58

What is the main purpose of a hypothesis test?

Accepted Answer

To determine whether there is sufficient evidence to reject a claim about a population parameter.

Answer

To predict future outcomes.

Answer

To estimate the value of a population parameter.

Question 59

Which of the following assumptions is required for conducting a chi-squared test of independence?

Accepted Answer

The expected frequency of each cell should be at least 5.

Answer

The sample size must be large.

Answer

The data must be normally distributed.

Question 60

A researcher wants to determine if there is a significant difference in the average height of male and female students in a school. Which hypothesis test would be most appropriate?

Accepted Answer

Two-sample t-test

Answer

Paired t-test

Answer

Chi-square test

Answer

One-sample t-test

Question 61

A company claims that the average lifespan of its batteries is 1000 hours. A consumer group conducts a study and finds that a sample of 50 batteries has an average lifespan of 980 hours with a standard deviation of 50 hours. What is the p-value for the hypothesis test that the true average lifespan is 1000 hours?

Accepted Answer

0.05 < p-value < 0.10

Answer

p-value > 0.10

Answer

p-value = 0.05

Answer

p-value < 0.01

Question 62

Which of the following is NOT a characteristic of a normal distribution?

Accepted Answer

Skewness

Answer

Bell-shaped curve

Answer

Symmetry

Answer

Mean, median, and mode are equal

Question 63

A researcher wants to study the relationship between the number of hours spent studying and the score on a test. Which type of regression analysis would be most appropriate?

Accepted Answer

Linear regression

Answer

Multiple regression

Answer

Logistic regression

Answer

Time series regression

Question 64

A company is testing a new drug to treat a disease. They randomly assign 100 patients to two groups: a treatment group and a control group. The treatment group receives the new drug, and the control group receives a placebo. After a month, they measure the improvement in symptoms for each patient. What type of study is this?

Accepted Answer

Randomized controlled trial

Answer

Observational study

Answer

Case-control study

Answer

Cohort study