1. What is multicollinearity in regression analysis and why is it a problem?
A. It is when the dependent variable is correlated with itself over time; it`s a problem because it violates assumptions of time series analysis.
B. It is high correlation among independent variables; it`s a problem because it makes it difficult to isolate the individual effect of each independent variable.
C. It is when residuals are not normally distributed; it`s a problem because it invalidates hypothesis tests.
D. It is when the variance of errors is not constant across observations; it`s a problem because it leads to inefficient estimators.
2. In forecasting, what is `seasonality`?
A. A long-term upward or downward movement in data.
B. Irregular fluctuations in data.
C. A pattern that repeats at regular intervals over time, typically within a year.
D. Random variations in data.
3. Which of the following is NOT a characteristic of the normal distribution?
A. Symmetric around the mean.
B. Unimodal (has one mode).
C. Skewed to the right.
D. Defined by two parameters: mean and standard deviation.
4. Why is it important to check assumptions of statistical tests before applying them?
A. To make the analysis process longer and more complex.
B. To ensure the test results are valid and reliable.
C. Because all statistical software requires assumption checking.
D. To increase the p-value and reject the null hypothesis more easily.
5. In the context of sampling, what is `sampling bias`?
A. A random error that occurs in every sample.
B. A systematic error that leads to a sample not representative of the population.
C. The difference between the sample mean and the population mean.
D. The size of the sample relative to the population.
6. What does a high correlation coefficient (close to +1 or -1) between two variables indicate?
A. Causation between the two variables.
B. A strong linear relationship between the two variables.
C. No relationship between the two variables.
D. A non-linear relationship between the two variables.
7. In time series analysis, what is `trend`?
A. Short-term fluctuations in data.
B. Regular seasonal patterns.
C. Long-term direction or movement in data.
D. Random noise in data.
8. Which of the following is NOT a primary function of statistics in economics and business?
A. Describing economic phenomena and business conditions.
B. Predicting future economic trends and business outcomes.
C. Controlling political elections.
D. Making informed decisions under uncertainty.
9. What type of data is `customer satisfaction rating on a scale of 1 to 5`?
A. Nominal data
B. Ordinal data
C. Interval data
D. Ratio data
10. What is the purpose of confidence intervals in statistical inference?
A. To determine the exact value of a population parameter.
B. To provide a range of plausible values for a population parameter.
C. To test hypotheses about population parameters.
D. To eliminate sampling error.
11. Which of the following is a measure of dispersion?
A. Mean
B. Median
C. Standard Deviation
D. Mode
12. What is the purpose of ANOVA (Analysis of Variance)?
A. To compare the means of two independent groups.
B. To compare the means of three or more groups.
C. To analyze the correlation between two variables.
D. To predict the value of a dependent variable.
13. Which measure of central tendency is most affected by outliers?
A. Median
B. Mode
C. Mean
D. Geometric Mean
14. Which distribution is often used to model the number of occurrences of an event in a fixed interval of time or space?
A. Normal distribution
B. Binomial distribution
C. Poisson distribution
D. Exponential distribution
15. Which statistical test is used to examine the association between two categorical variables?
A. T-test
B. ANOVA
C. Chi-squared test
D. Regression analysis
16. Which statistical method is best suited for comparing means of two independent groups?
A. Correlation analysis
B. Regression analysis
C. Independent samples t-test
D. Chi-squared test
17. In index numbers, what does a base period represent?
A. The most recent period in the data.
B. A reference period against which changes are measured.
C. The period with the highest value in the data.
D. The period with the lowest value in the data.
18. What is the difference between a population and a sample in statistics?
A. A population is always larger than a sample.
B. A sample is a subset of the population.
C. A population is used for descriptive statistics, while a sample is for inferential statistics.
D. All of the above.
19. In statistical hypothesis testing, what does the null hypothesis typically represent?
A. The researcher`s belief about the population.
B. The alternative hypothesis.
C. A statement of no effect or no difference.
D. A statement that is always true.
20. What is the purpose of stratified sampling?
A. To select samples randomly without any specific structure.
B. To divide the population into subgroups (strata) and then randomly sample from each stratum.
C. To sample every nth member of the population.
D. To select samples based on convenience.
21. Which type of chart is most suitable for showing the distribution of a continuous variable?
A. Pie chart
B. Bar chart
C. Histogram
D. Scatter plot
22. What does the Central Limit Theorem state?
A. The mean of any sample is always equal to the population mean.
B. The standard deviation of the sample mean is equal to the population standard deviation.
C. For a sufficiently large sample size, the distribution of sample means will be approximately normal, regardless of the population`s distribution.
D. The sample median is always a better estimator of central tendency than the sample mean.
23. Which of the following is an example of time series data?
A. Customer ages at a single point in time.
B. Sales revenue recorded quarterly for the past five years.
C. Survey responses from a one-time survey.
D. Cross-sectional data of company profits in a single year.
24. What is the difference between Type I and Type II error in hypothesis testing?
A. Type I error is rejecting a false null hypothesis; Type II error is failing to reject a true null hypothesis.
B. Type I error is failing to reject a false null hypothesis; Type II error is rejecting a true null hypothesis.
C. Type I error is rejecting a true null hypothesis; Type II error is failing to reject a false null hypothesis.
D. Type I and Type II errors are the same thing but referred to differently in different fields.
25. What is heteroscedasticity in regression analysis?
A. Non-linear relationship between variables.
B. Correlation between independent variables.
C. Unequal variance of errors across different levels of independent variables.
D. Non-normality of residuals.
26. What is the role of p-value in hypothesis testing?
A. It represents the probability that the null hypothesis is true.
B. It is the significance level chosen before conducting the test.
C. It measures the strength of the alternative hypothesis.
D. It is the probability of observing the data (or more extreme data) if the null hypothesis is true.
27. What is the purpose of data visualization in statistical analysis?
A. To perform complex statistical calculations.
B. To make data more understandable and identify patterns.
C. To replace statistical analysis entirely.
D. To store large datasets.
28. What does R-squared measure in regression analysis?
A. The statistical significance of the independent variables.
B. The strength and direction of the relationship between variables.
C. The proportion of variance in the dependent variable that is predictable from the independent variables.
D. The probability of rejecting the null hypothesis.
29. What is the purpose of regression analysis in economics and business?
A. To summarize data with charts and graphs.
B. To describe the distribution of a single variable.
C. To model the relationship between a dependent variable and one or more independent variables.
D. To calculate probabilities of events.
30. What is the role of statistical significance in hypothesis testing?
A. To prove the alternative hypothesis is true.
B. To indicate the practical importance of the findings.
C. To provide evidence against the null hypothesis.
D. To ensure the sample is representative of the population.
