Statistics for Sixth Form: Interactive Learning Quizzes

Question 1

To obtain unbiased consumer feedback, which sampling method should a market research company use to ensure a representative sample that accurately reflects the population's preferences?

Accepted Answer

Simple random sampling

Answer

Systematic sampling

Answer

Quota sampling

Answer

Convenience sampling

Question 2

You come across a claim in an online article that states '95% of teenagers use social media daily.' How should you, as a critical reader, evaluate the reliability and credibility of this claim?

Accepted Answer

Examine the source of the claim, considering its credibility, expertise, and potential biases.

Answer

Accept the claim without question, as it appears in a reputable online source.

Answer

Dismiss the claim as false without further investigation, assuming it is exaggerated or sensationalized.

Answer

Focus solely on the reported percentage (95%) without questioning the sample size or methodology used to obtain it.

Question 3

How does increasing the sample size affect the accuracy and reliability of statistical conclusions? Give a specific example to demonstrate.

Accepted Answer

Increases both accuracy and reliability

Answer

Increases accuracy but decreases reliability

Answer

Has no impact on accuracy or reliability

Answer

Decreases both accuracy and reliability

Question 4

Which of the following ethical principles is essential in statistical research?

Accepted Answer

Informed consent

Accepted Answer

Privacy

Accepted Answer

Objectivity

Answer

Exploitation

Question 5

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

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 6

In a normal distribution, what percentage of data falls within one standard deviation of the mean?

Accepted Answer

Approximately 68%

Answer

Approximately 34%

Answer

Approximately 95%

Answer

Approximately 99%

Question 7

Which probability distribution is used to model the number of successes in a sequence of independent Bernoulli trials?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Poisson distribution

Answer

Exponential distribution

Question 8

What is the hypothesis that is assumed to be true in a hypothesis test?

Accepted Answer

The null hypothesis

Answer

The alternative hypothesis

Answer

The research hypothesis

Answer

The statistical hypothesis

Question 9

In a linear regression model, what variable is affected by changes in the independent variable?

Accepted Answer

Dependent variable

Answer

Independent variable

Answer

Constant variable

Answer

Control variable

Question 10

What is the difference between a population parameter and a sample statistic?

Accepted Answer

Population parameters are fixed values for the population, while sample statistics are estimates of population parameters derived from sample data

Answer

Population parameters are estimates of population parameters derived from sample data, while sample statistics are fixed values for the population

Answer

Population parameters are always known, while sample statistics are always unknown

Answer

Sample statistics are always known, while population parameters are always unknown

Question 11

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

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 12

The probability of rolling a 6 on a standard six-sided die is:

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 13

A normal distribution is characterized by a:

Accepted Answer

Symmetrical bell-shaped curve

Answer

Skewness

Answer

Kurtosis

Answer

Bimodality

Question 14

Which of the following tests is used to determine if there is a statistically significant difference between two population means?

Accepted Answer

T-test

Answer

Chi-squared test

Answer

ANOVA

Answer

Regression analysis

Question 15

The correlation coefficient measures the:

Accepted Answer

Strength and direction of linear relationship

Answer

Level of statistical significance

Answer

Probability of one variable predicting another

Answer

Dispersion of data

Question 16

Which of the following sampling methods is most likely to produce a skewed sample?

Accepted Answer

Convenience sampling

Answer

Simple random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Question 17

The interquartile range (IQR) is a measure of:

Accepted Answer

Variability

Answer

Central tendency

Answer

Skewness

Answer

Kurtosis

Question 18

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

Accepted Answer

Spearman's rank correlation coefficient

Answer

T-test

Answer

ANOVA

Answer

Chi-squared test

Question 19

The p-value represents:

Accepted Answer

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

Answer

The level of statistical significance

Answer

The correlation coefficient

Answer

The slope of the regression line

Question 20

Which of the following is the most accurate method for collecting data from a sample that truly represents the entire population?

Accepted Answer

Stratified sampling

Answer

Convenience sampling

Answer

Quota sampling

Answer

Snowball sampling

Question 21

In hypothesis testing, which hypothesis represents the initial assumption that is tested?

Accepted Answer

Null hypothesis

Answer

Alternative hypothesis

Answer

Research hypothesis

Answer

Experimental hypothesis

Question 22

Which measure is used to quantify the spread or variability within a data set?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Range

Answer

Correlation coefficient

Question 23

In a regression equation, what does the coefficient of the independent variable represent?

Accepted Answer

Average change in the dependent variable for a unit change in the independent variable

Answer

Predicted value of the dependent variable when the independent variable is zero

Answer

Strength of the relationship between the variables

Answer

Correlation between the variables

Question 24

Which non-parametric test is suitable for comparing the medians of two independent samples?

Accepted Answer

Mann-Whitney U test

Answer

Kolmogorov-Smirnov test

Answer

Chi-square test

Answer

t-test

Question 25

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

Accepted Answer

Standard Deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 26

Which hypothesis test is suitable for determining whether there is a significant difference between the mean scores of two independent groups?

Accepted Answer

Two-sample t-test

Answer

One-sample t-test

Answer

Chi-square test

Answer

ANOVA

Question 27

In a linear regression model, an R² value of 0.85 indicates that:

Accepted Answer

85% of the variation in the dependent variable is explained by the independent variable.

Answer

The model has a poor fit.

Answer

The model has a perfect fit.

Answer

The coefficient of determination is unreliable.

Question 28

Which method of data collection involves observing and recording behaviour in its natural context?

Accepted Answer

Observation

Answer

Survey

Answer

Interview

Answer

Experiment

Question 29

Given the dataset {5, 7, 9, 11, 13}, what is the range?

Accepted Answer

13

Answer

5

Answer

6

Answer

18

Question 30

In a scatterplot, a negative correlation indicates that:

Accepted Answer

As the value of one variable increases, the value of the other variable decreases.

Answer

There is no relationship between the variables.

Answer

As the value of one variable increases, the value of the other variable also increases.

Answer

As the value of one variable decreases, the value of the other variable increases.

Question 31

Which measure of central tendency is most appropriate for describing the center of a distribution of data on the heights of adult males in a certain population?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 32

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

Accepted Answer

0.5

Answer

0.25

Answer

0.75

Answer

1

Question 33

In a hypothesis test, what does committing a Type I error involve?

Accepted Answer

Rejecting the null hypothesis when it is true

Answer

Accepting the null hypothesis when it is false

Answer

Failing to reject the null hypothesis when it is false

Answer

Rejecting the null hypothesis correctly

Question 34

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

Accepted Answer

The change in y for a one-unit change in x

Answer

The average value of y

Answer

The correlation coefficient between x and y

Answer

The intercept of the regression line

Question 35

Which of the following sampling methods is most likely to produce a sample that reflects the characteristics of the entire population?

Accepted Answer

Simple random sampling

Answer

Stratified sampling

Answer

Convenience sampling

Answer

Systematic sampling

Question 36

What does the interquartile range (IQR) measure?

Accepted Answer

Spread or variability

Answer

Center or location

Answer

Skewness

Answer

Kurtosis

Question 37

Which probability distribution is most likely to be skewed right?

Accepted Answer

Exponential distribution

Answer

Uniform distribution

Answer

Normal distribution

Answer

Binomial distribution

Question 38

Which of the following is the measure of central tendency that is unaffected by extreme values?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 39

Which of the following is NOT a key assumption of hypothesis testing?

Accepted Answer

The hypothesis is always true

Answer

The data is normally distributed

Answer

The sample size is sufficiently large

Answer

The variables are independent

Question 40

A scatter plot shows a strong positive correlation between two variables. Which of the following regression models would most likely be appropriate?

Accepted Answer

Linear regression

Answer

Logarithmic regression

Answer

Exponential regression

Answer

Multiple regression

Question 41

Which of the following sampling methods is most likely to produce an unbiased sample?

Accepted Answer

Simple random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Answer

Convenience sampling

Question 42

A survey asks respondents to rate their satisfaction with a product on a scale of 1 to 5. What type of data is being collected?

Accepted Answer

Ordinal

Answer

Categorical

Answer

Interval

Answer

Ratio

Question 43

A medical study compares the effectiveness of two different treatments for a disease. The study uses a blinded design. What does this mean?

Accepted Answer

Neither the participants nor the researchers know which treatment is being given

Answer

Only the participants know which treatment they are receiving

Answer

Only the researchers know which treatment is being given

Answer

Both the participants and the researchers know which treatment is being given

Question 44

A hypothesis test has a significance level of 0.05. What does this mean?

Accepted Answer

There is a 5% chance of rejecting the null hypothesis when it is true

Answer

There is a 5% chance of accepting the null hypothesis when it is false

Answer

There is a 95% chance of rejecting the null hypothesis when it is true

Answer

There is a 95% chance of accepting the null hypothesis when it is false

Question 45

Which of the following is NOT a type of parametric statistical model?

Accepted Answer

Cluster analysis

Answer

Linear regression

Answer

Logistic regression

Answer

Time series model

Question 46

Which assumption is NOT required for a simple linear regression model?

Accepted Answer

Normally distributed errors

Answer

Linear relationship between variables

Answer

Equal variability of residuals

Answer

Uncorrelated errors

Question 47

A sample space is the...

Accepted Answer

Set of all possible outcomes of an experiment

Answer

Set of all possible values of a random variable

Answer

Set of all possible events in an experiment

Answer

Set of all possible distributions of a random variable

Question 48

The probability of an event occurring can be represented by a number between:

Accepted Answer

0 and 1

Answer

-1 and 1

Answer

0 and 100

Answer

-100 and 100

Question 49

The coefficient of determination (R-squared) in regression analysis measures:

Accepted Answer

The proportion of variation in the dependent variable explained by the independent variable

Answer

The strength of the relationship between the dependent and independent variables

Answer

The probability of making a prediction error

Answer

The significance of the regression model

Question 50

Measures of central tendency do NOT include:

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 51

On a standard six-sided die, the probability of rolling a 6 is:

Accepted Answer

1 / 6

Answer

1 / 3

Answer

1 / 4

Answer

1 / 2

Question 52

In a statistical test, the null hypothesis is:

Accepted Answer

The hypothesis that is assumed to be true

Answer

The hypothesis being tested

Answer

The hypothesis that is rejected if the p-value is significant

Answer

The hypothesis that is accepted if the p-value is not significant

Question 53

The purpose of a scatterplot is to:

Accepted Answer

Illustrate the relationship between two variables

Answer

Show the distribution of a single variable

Answer

Predict the value of one variable from another

Answer

Test the significance of a relationship

Question 54

A data collection method involving selecting a portion of a population that represents the entire population is known as:

Accepted Answer

Random sampling

Answer

Systematic sampling

Answer

Stratified sampling

Answer

Convenience sampling

Question 55

In a regression analysis, which measure indicates the strength and direction of the linear relationship between the variables?

Accepted Answer

Correlation Coefficient (r)

Answer

Coefficient of Determination (R-squared)

Answer

Slope of the Regression Line

Answer

Intercept of the Regression Line

Question 56

Which of the following is NOT a valid method of data collection?

Accepted Answer

Informed speculation

Answer

Surveys

Answer

Interviews

Answer

Experiments

Question 57

What is the probability of rolling a '6' on a fair six-sided die?

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 58

What is the primary purpose of hypothesis testing?

Accepted Answer

To reject a hypothesis if there is sufficient evidence against it

Answer

To prove a hypothesis is true

Answer

To collect data

Answer

To estimate population parameters

Question 59

Which of the following is a measure of the strength and direction of a linear relationship?

Accepted Answer

Correlation coefficient

Answer

Regression coefficient

Answer

Standard deviation

Answer

Mean

Question 60

What is the expected value of a random variable X with probability distribution P(X = x) = 1/3 for x = 1, 2, 3?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 61

Which of the following is a Type I error?

Accepted Answer

Rejecting a true null hypothesis

Answer

Accepting a false null hypothesis

Answer

Accepting a true alternative hypothesis

Answer

Rejecting a false alternative hypothesis

Question 62

What is the purpose of a confidence interval?

Accepted Answer

To estimate a population parameter with a specified level of confidence

Answer

To prove a hypothesis is true

Answer

To reject a hypothesis if there is evidence against it

Answer

To collect data

Question 63

Which measure is NOT used to describe the central tendency of a data set?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Range

Question 64

In a binomial distribution with parameters n and p, what is the formula for the probability of exactly k successes?

Accepted Answer

(n k) * p^k * (1-p)^(n-k)

Answer

(n k) * p^k * (1-p)^(k-n)

Answer

k * p^k * (1-p)^(n-k)

Answer

k * p^k * (1-p)^(n+k)