Statistics for Year 13: Master Statistical Concepts and Techniques

Question 1

Question:
How has technology revolutionized the way we collect, analyze, and draw conclusions from statistical data?

Accepted Answer

Technology has accelerated data collection, enabling us to gather vast amounts of data swiftly and efficiently.

Accepted Answer

Technology has empowered us with more advanced statistical analyses, allowing us to uncover intricate relationships within data.

Answer

Technology has automated statistical interpretation, eliminating the need for human judgment.

Answer

Technology has rendered statistical methods obsolete, as data can now be analyzed without statistical knowledge.

Question 2

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

Accepted Answer

(d) Non-constant variance of residuals

Answer

(a) Normality of residuals

Answer

(b) Independence of residuals

Answer

(c) Zero mean for residuals

Question 3

Which sampling method involves dividing the population into subgroups based on a specific characteristic and then randomly selecting individuals from each subgroup?

Accepted Answer

Stratified sampling

Answer

Simple random sampling

Answer

Cluster sampling

Answer

Systematic sampling

Question 4

In a hypothesis test with a significance level of 0.05, what decision should be made if the p-value is 0.03?

Accepted Answer

Reject the null hypothesis

Answer

Fail to reject the null hypothesis

Answer

Accept the alternative hypothesis

Answer

Insufficient information to conclude

Question 5

Which probability distribution models the number of successes in a sequence of independent experiments with a constant probability of success?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Poisson distribution

Answer

Exponential distribution

Question 6

What is the fundamental difference between a population and a sample?

Accepted Answer

A population represents the entire group under study, while a sample is a smaller subset.

Answer

A sample represents the entire group under study, while a population is a smaller subset.

Answer

A population is a group of people, while a sample is a group of objects.

Answer

There is no distinction between a population and a sample.

Question 7

Which visual representation effectively displays the distribution of data, including both central tendency and variability?

Accepted Answer

Histogram

Answer

Bar chart

Answer

Scatter plot

Answer

Pie chart

Question 8

What is the primary purpose of calculating a confidence interval?

Accepted Answer

Estimating the population parameter with a specified level of certainty

Answer

Testing a hypothesis about the population parameter

Answer

Generating a precise estimate of the sample mean

Answer

Determining the probability of obtaining a specific sample

Question 9

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

Accepted Answer

Mean

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 10

In a regression model used to predict house prices based on size, the slope coefficient of the regression line is positive. What does this indicate?

Accepted Answer

As the size of the house increases, the predicted price also increases.

Answer

As the size of the house increases, the predicted price decreases.

Answer

There is no relationship between the size of the house and the predicted price.

Answer

The predicted price is independent of the size of the house.

Question 11

For a confidence interval constructed for a population proportion with a confidence level of 95%, what does this level indicate?

Accepted Answer

There is a 95% probability that the true proportion lies within the interval.

Answer

There is a 95% probability that the sample proportion lies within the interval.

Answer

The true proportion will definitely lie within the interval.

Answer

The sample proportion will definitely lie within the interval.

Question 12

Which of the following statistical tests is commonly used to test the independence of two categorical variables?

Accepted Answer

Chi-square test

Answer

t-test

Answer

ANOVA

Answer

Regression analysis

Question 13

A scatterplot displays a strong positive correlation between two variables. What can be concluded from this?

Accepted Answer

As one variable increases, the other variable also tends to increase.

Answer

As one variable increases, the other variable tends to decrease.

Answer

There is no relationship between the two variables.

Answer

The two variables are independent.

Question 14

Which of the following is a measure of spread?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 15

Which of the following probability distributions is used to model the time between arrivals of customers in a queue?

Accepted Answer

Exponential distribution

Answer

Binomial distribution

Answer

Normal distribution

Answer

Poisson distribution

Question 16

Which of the following is a disadvantage of using stratified sampling?

Accepted Answer

It can be more difficult to implement than simple random sampling.

Answer

It can be less representative of the population.

Answer

It can increase sampling error.

Answer

It can give each member of the population an unequal chance of being selected.

Question 17

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

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 18

Which of the following is NOT an assumption of the normal distribution?

Accepted Answer

Unbounded

Answer

Symmetrical

Answer

Bell-shaped

Answer

Constant mean

Question 19

A data set is skewed to the right. Which of the following would be the most appropriate measure of central tendency to use?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Standard deviation

Question 20

A linear regression model has a coefficient of determination (R-squared) of 0.85. What does this value indicate?

Accepted Answer

The model explains 85% of the variation in the dependent variable.

Answer

The model explains 15% of the variation in the dependent variable.

Answer

The model is not significant.

Answer

The model is perfectly accurate.

Question 21

Define the sampling distribution and explain its importance in making statistical inferences.

Accepted Answer

The probability distribution of sample means from all possible samples of a given size from a population.

Answer

The distribution of individual data points within a sample.

Answer

A method for selecting a representative sample from a population.

Answer

A statistical test used to compare the means of two different populations.

Question 22

Rolling a fair standard six-sided die once, what is the probability of obtaining a 6?

Accepted Answer

1/6

Answer

1/3

Answer

1/2

Answer

2/3

Question 23

Which distribution is symmetrical with respect to its mean?

Accepted Answer

1/Normal distribution

Answer

2/Binomial distribution

Answer

3/Poisson distribution

Answer

4/Exponential distribution

Question 24

In hypothesis testing, what does the null hypothesis posit?

Accepted Answer

There is no significant difference between the groups under examination

Answer

There is a significant difference between the groups under examination

Answer

The population mean is equal to a known value

Answer

The population variance is equal to a known value

Question 25

Which method of sampling involves selecting individuals randomly from the population?

Accepted Answer

1/Simple random sampling

Answer

2/Stratified sampling

Answer

3/Cluster sampling

Answer

4/Convenience sampling

Question 26

What is the primary function of a confidence interval?

Accepted Answer

Estimating a population parameter with a certain level of confidence

Answer

Testing the hypothesis that a population parameter is equal to a known value

Answer

Comparing the means of two populations

Answer

Predicting future observations

Question 27

In a two-sample t-test, what is the null hypothesis?

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 28

Which of the following is a measure of central tendency that represents the average value in a dataset?

Accepted Answer

Mean

Answer

Variance

Answer

Percentile

Answer

Standard deviation

Question 29

Which of the following types of bias can occur when individuals in a sample are more likely to respond to a survey than others?

Accepted Answer

Non-response bias

Answer

Selection bias

Answer

Response bias

Answer

Measurement bias

Question 30

In a hypothesis test, the null hypothesis states that:

Accepted Answer

There is no significant difference or relationship

Answer

The assumed relationship between variables is true

Answer

The assumed difference between groups is significant

Answer

The alternative hypothesis is false

Question 31

What type of error occurs when the null hypothesis is rejected even though it is true?

Accepted Answer

Type I error

Answer

Type II error

Answer

False positive

Answer

False negative

Question 32

A confidence interval with a confidence level of 95% implies that:

Accepted Answer

There is a 95% probability that the true population parameter lies within the interval

Answer

There is a 95% probability that the sample mean lies within the interval

Answer

There is a 5% probability that the true population parameter lies outside the interval

Answer

There is a 95% probability that the true population parameter lies outside the interval

Question 33

To determine if there is a significant difference in mean scores between two groups on a test, which statistical test is appropriate?

Accepted Answer

Two-sample t-test

Answer

One-sample t-test

Answer

Analysis of variance (ANOVA)

Answer

Chi-square test

Question 34

What type of distribution is characterized by a bell-shaped curve?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Uniform distribution

Question 35

Which data type is used to represent the gender of students?

Accepted Answer

Qualitative

Answer

Quantitative

Answer

Discrete

Answer

Continuous

Question 36

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

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 37

Which hypothesis test is used to determine if there is a significant relationship between two categorical variables?

Accepted Answer

Chi-square test

Answer

T-test

Answer

ANOVA

Answer

Regression analysis

Question 38

What is the main purpose of exploratory data analysis?

Accepted Answer

To identify patterns and trends

Answer

To test hypotheses

Answer

To make predictions

Answer

To draw conclusions

Question 39

Which graphical representation is used to display the relationship between two continuous variables?

Accepted Answer

Scatterplot

Answer

Pie chart

Answer

Histogram

Answer

Bar chart

Question 40

Which probability distribution is used to model the number of successes in a sequence of independent trials, where each trial has a constant probability of success?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Poisson distribution

Answer

Uniform distribution

Question 41

In a hypothesis test, what is the null hypothesis?

Accepted Answer

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

Answer

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

Answer

The hypothesis that the data supports the research question.

Answer

The hypothesis that the data does not support the research question.

Question 42

Which of the following is a non-parametric test that can be used to compare the medians of two independent groups?

Accepted Answer

Wilcoxon rank-sum test

Answer

Chi-squared test

Answer

t-test

Answer

ANOVA

Question 43

What is the difference between a population and a sample?

Accepted Answer

A population is the entire group of individuals being studied, while a sample is a subset of the population.

Answer

A sample is the entire group of individuals being studied, while a population is a subset of the sample.

Answer

A population and a sample are the same thing.

Answer

There is no difference between a population and a sample.

Question 44

Identify the measure of central tendency that describes the most frequently occurring value in a dataset.

Accepted Answer

Mode

Answer

Mean

Answer

Median

Answer

Standard Deviation

Question 45

Which probability distribution exhibits a bell-shaped curve with equal tails?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Uniform distribution

Question 46

Which condition is essential for using the t-test to compare population means?

Accepted Answer

The sample must be drawn randomly

Answer

The sample size must be extremely large

Answer

The population standard deviation must be known

Answer

The population must be normally distributed

Question 47

In hypothesis testing, what outcome occurs when there is insufficient evidence to reject the null hypothesis?

Accepted Answer

Fail to reject the null hypothesis

Answer

Accept the alternative hypothesis

Answer

Reject the null hypothesis

Answer

Accept the null hypothesis

Question 48

A multiple regression model has an R-squared value of 0.7. What proportion of the dependent variable's variance is explained by the independent variables?

Accepted Answer

70%

Answer

30%

Answer

50%

Answer

90%

Question 49

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

Accepted Answer

Simple random sampling

Answer

Systematic sampling

Answer

Convenience sampling

Answer

Quota sampling

Question 50

A correlation coefficient of 0.9 indicates a:

Accepted Answer

Strong positive correlation

Answer

Weak positive correlation

Answer

Strong negative correlation

Answer

Weak negative correlation

Question 51

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

Accepted Answer

Range

Answer

Arithmetic Mean

Answer

Median

Answer

Mode

Question 52

From a school of 1000 students, where 60% are male, a sample of 50 students is taken. What is the probability of selecting a male student?

Accepted Answer

0.6

Answer

0.3

Answer

0.5

Answer

0.7

Question 53

Which of the following is the formula for calculating the z-score?

Accepted Answer

(x - μ) / σ

Answer

(μ - x) / σ

Answer

σ / (x - μ)

Answer

σ / (μ - x)

Question 54

In a hypothesis test, which hypothesis is assumed to be true?

Accepted Answer

The null hypothesis

Answer

The alternative hypothesis

Answer

The research hypothesis

Answer

The experimental hypothesis

Question 55

What is the distinction between a parameter and a statistic?

Accepted Answer

A parameter is a value calculated from a population, while a statistic is a value calculated from a sample

Answer

A statistic is a value calculated from a population, while a parameter is a value calculated from a sample

Answer

A parameter is a fixed value, while a statistic is a random variable

Answer

A statistic is a fixed value, while a parameter is a random variable

Question 56

What is the purpose of a confidence interval?

Accepted Answer

To provide an estimate of the population parameter with a specified level of confidence

Answer

To test whether a hypothesis is true

Answer

To determine the sample size needed for a study

Answer

To calculate the probability of a particular outcome

Question 57

Which type of statistical test is used to compare the means of two independent samples?

Accepted Answer

t-test

Answer

ANOVA

Answer

Chi-square test

Answer

F-test

Question 58

What does the p-value of a hypothesis test represent?

Accepted Answer

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

Answer

The probability of rejecting the null hypothesis

Answer

The probability of accepting the null hypothesis

Answer

The level of significance of the test

Question 59

Identify the option that does not represent a valid type of statistical distribution:

Accepted Answer

Equilateral distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Normal distribution

Question 60

When rolling a fair six-sided die, what is the probability of obtaining a 6?

Accepted Answer

1/6

Answer

1/3

Answer

1/4

Answer

1/5

Question 61

Which sampling technique is most suitable for obtaining a representative sample of a population?

Accepted Answer

Simple random sampling

Answer

Convenience sampling

Answer

Quota sampling

Answer

Snowball sampling

Question 62

What is the primary goal of conducting a hypothesis test?

Accepted Answer

To determine if sufficient evidence exists to reject a null hypothesis

Answer

To verify existing assumptions

Answer

To predict future outcomes

Answer

To identify the population mean and standard deviation

Question 63

Which statistical measure is used to quantify the spread or dispersion of a dataset?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 64

State the formula for calculating the mean of a sample:

Accepted Answer

Σx / n

Answer

Σx / (n-1)

Answer

(Σx)² / n

Answer

x - n / Σx