Statistics 1: Master the Basics of Data Analysis and Probability

Question 1

For non-normally distributed data, which statistical test is typically used to compare two independent groups?

Accepted Answer

Mann-Whitney U test

Answer

T-test

Answer

F-test

Answer

Chi-squared test

Question 2

Which probability distribution is used to model continuous data that can take any value within a range?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Chi-squared distribution

Question 3

In hypothesis testing, the alternative hypothesis (Ha) is the hypothesis that:

Accepted Answer

Proposes an alternative to the null hypothesis that the researcher aims to support.

Answer

Assumes the null hypothesis is true unless proven otherwise.

Answer

Becomes true if the null hypothesis is rejected.

Answer

Is always true, regardless of the sample data.

Question 4

A survey of 100 students from a school of 1000 found an average height of 170 cm. If the standard deviation of all student heights is 10 cm, what's the standard error of the mean height?

Accepted Answer

1 cm

Answer

10 cm

Answer

100 cm

Answer

1000 cm

Question 5

Which sampling method relies on selecting participants who are easily accessible, rather than ensuring they represent the entire population?

Accepted Answer

Convenience sampling

Answer

Simple random sampling

Answer

Systematic sampling

Answer

Stratified sampling

Question 6

Identify the non-probability sampling method from the options below:

Accepted Answer

Convenience sampling

Answer

Simple random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Question 7

What distinguishes quota sampling from other sampling methods?

Accepted Answer

Ensuring the sample reflects the population's characteristics

Answer

Selecting every nth member of the population

Answer

Providing an equal chance of selection for all population members

Answer

Selecting a sample from a hard-to-reach population

Question 8

Which of the following is NOT a type of probability sampling?

Accepted Answer

Quota sampling

Answer

Simple random sampling

Answer

Systematic sampling

Answer

Stratified sampling

Question 9

A company's annual profits have a skewed distribution, with a few unusually high profits. Which measure of central tendency would be most suitable for this data?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 10

Which probability distribution is used to model continuous random variables?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Uniform distribution

Question 11

Which fundamental characteristic defines a probability distribution?

Accepted Answer

The sum of probabilities for all possible outcomes equals 1.

Answer

The probability distribution is always symmetrical.

Answer

The mean of the probability distribution is always 0.

Question 12

Which of the following is NOT a measure of central tendency? Measures of central tendency describe the average or typical value in a data set.

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 13

In a survey, researchers randomly selected 100 people from a list of 1000 registered voters. What sampling method did they use?

Accepted Answer

Simple random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Answer

Convenience sampling

Question 14

Which of the following is NOT a type of hypothesis testing in statistics?

Accepted Answer

Correlation analysis

Answer

One-sample t-test

Answer

Two-sample t-test

Answer

Analysis of variance (ANOVA)

Question 15

Which of the following is **not** a factor that can affect the validity of a statistical inference?

Accepted Answer

The researcher's expectations

Answer

Sample size

Answer

Sampling method

Answer

Measurement error

Question 16

Which probability distribution is used to model the time between events occurring randomly at a constant average rate?

Accepted Answer

Poisson distribution

Answer

Binomial distribution

Answer

Normal distribution

Answer

Uniform distribution

Question 17

Which data collection method allows researchers to observe behavior without directly interacting with participants?

Accepted Answer

Observational study

Answer

Interview

Answer

Participant observation

Question 18

In a research study, a convenience sampling method is used to select participants from a shopping mall. What is a potential limitation of using this non-probability sampling method?

Accepted Answer

Findings may be biased towards certain groups of people who frequent shopping malls.

Answer

Findings can be accurately generalized to the entire population.

Answer

Findings can be generalized to other shopping malls with similar characteristics.

Question 19

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

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 20

Which statistical method is employed to make predictions based on a sample?

Accepted Answer

Regression analysis

Answer

Hypothesis testing

Answer

Correlation analysis

Answer

Chi-squared test

Question 21

A confidence interval represents a range of values that is likely to contain:

Accepted Answer

The population mean

Answer

The sample mean

Answer

The population standard deviation

Answer

The sample size

Question 22

Which sampling method involves selecting every nth individual from a population in a sequential order?

Accepted Answer

Systematic sampling

Answer

Simple random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Question 23

The chi-squared test is primarily used to determine:

Accepted Answer

Whether two categorical variables are independent

Answer

Whether the population mean is equal to a specified value

Answer

If two variables are correlated

Answer

If a sample is drawn from a normal distribution

Question 24

What is the main purpose of using descriptive statistics in data analysis?

Accepted Answer

To simplify and present data in a clear and understandable manner

Answer

To draw conclusions about a larger group based on a smaller sample

Answer

To find patterns and trends in data

Question 25

Which of the following is NOT a type of inferential statistical test?

Accepted Answer

Data visualization

Answer

Hypothesis testing

Answer

Regression analysis

Answer

Correlation analysis

Question 26

What is the probability of rolling a 6 on a standard fair die?

Accepted Answer

1/6

Answer

1/4

Answer

1/3

Answer

1/5

Question 27

What is the null hypothesis in a statistical test?

Accepted Answer

The hypothesis that states there is no significant difference or relationship.

Answer

The hypothesis that states there is a significant difference or relationship.

Answer

The hypothesis that the researcher is trying to prove.

Answer

The hypothesis that the researcher is trying to disprove.

Question 28

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

Accepted Answer

The errors have equal variance (homoscedasticity).

Answer

The relationship between the independent and dependent variables is linear.

Answer

The errors are normally distributed.

Answer

The errors are independent.

Question 29

When rolling a standard six-sided die, what is the probability of obtaining an even number?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

1/6

Question 30

For a two-tailed test with a sample size of 50 and a significance level of 0.05, what is the critical value?

Accepted Answer

±1.96

Answer

±2.33

Answer

±2.58

Answer

±3.00

Question 31

What is the distinction between a parameter and a statistic?

Accepted Answer

A parameter is a population characteristic, while a statistic is a sample characteristic.

Answer

A statistic is a population characteristic, while a parameter is a sample characteristic.

Answer

They are the same thing.

Answer

There is no difference.

Question 32

In random sampling, every individual in the population has an equal chance of being chosen. True or False?

Accepted Answer

True

Answer

False

Question 33

In hypothesis testing, the null hypothesis proposes:

Accepted Answer

No significant difference between groups

Answer

Significant difference between groups

Answer

The two groups are identical

Answer

The two groups are different

Question 34

Which of the following variables is **not** a quantitative variable?

Accepted Answer

Gender

Answer

Age

Answer

Height

Answer

Weight

Question 35

Which of the following is a measure of **variability**?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 36

What is the standard error of the mean for a sample of size n with a population standard deviation of σ?

Accepted Answer

σ/√n

Answer

σ²n

Answer

n/σ

Answer

√n/σ

Question 37

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

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 38

Given the probability of an event as 0.6, what is the probability of its complement?

Accepted Answer

0.4

Answer

0.3

Answer

0.7

Answer

0.5

Question 39

Which of the following is the correct formula for calculating standard deviation?

Accepted Answer

√[Σ(X - μ)² / (N - 1)]

Answer

Σ(X - μ) / N

Answer

Σ(X²/N) - μ²

Answer

Σ(X - μ) / N²

Question 40

What is the primary purpose of using a scatter plot?

Accepted Answer

To visualize the relationship between two variables.

Answer

To summarize data.

Answer

To make predictions.

Question 41

Which of the following is a type of probability sampling technique?

Accepted Answer

Stratified sampling

Answer

Frequency distribution

Answer

Mean

Answer

Histogram

Question 42

Explain the difference between a population and a sample.

Accepted Answer

A population is the entire group of individuals or objects of interest, while a sample is a subset of the population selected to represent the entire group.

Answer

A population is a theoretical concept, while a sample is an actual group of individuals.

Answer

A sample is the entire group of individuals or objects of interest, while a population is a subset of the sample.

Question 43

What is a key benefit of using a sampling distribution?

Accepted Answer

To make inferences about a population based on sample data.

Answer

To increase the accuracy of data.

Answer

To simplify data analysis.

Answer

To reduce the cost of research.

Question 44

What is the role of the significance level (α) in hypothesis testing?

Accepted Answer

To determine the probability of rejecting the null hypothesis when it is true (Type I error).

Answer

To determine the probability of accepting the null hypothesis when it is false (Type II error).

Answer

To calculate the p-value.

Question 45

What is the primary purpose of a confidence interval?

Accepted Answer

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

Answer

To determine the probability of an event.

Answer

To test the significance of a difference between two groups.