1. Time series analysis is primarily used for:
A. Comparing groups at a single point in time.
B. Analyzing data collected over time to identify patterns and trends.
C. Examining relationships between variables at a single point in time.
D. Categorical data analysis.
2. What is the role of statistics in quality control in manufacturing?
A. To increase production speed regardless of quality.
B. To monitor and improve production processes, identify defects, and ensure product consistency.
C. To replace manual inspection entirely.
D. To make products more expensive.
3. What is multicollinearity in regression analysis?
A. A perfect linear relationship between the dependent and independent variable.
B. A high correlation between two or more independent variables.
C. A lack of correlation between the independent variables.
D. Non-linearity in the data.
4. What is a `null hypothesis` in hypothesis testing?
A. The hypothesis that the researcher wants to prove.
B. A statement of no effect or no difference, which is tested against the alternative hypothesis.
C. The hypothesis that is always true.
D. The hypothesis based on sample data.
5. Which of the following is NOT a measure of central tendency?
A. Mean
B. Median
C. Mode
D. Standard Deviation
6. What is the significance level (alpha, α) in hypothesis testing?
A. The probability of making a Type II error.
B. The probability of rejecting a true null hypothesis (Type I error).
C. The power of the test.
D. The confidence level.
7. Which of the following is NOT a common type of chart used for data visualization in business?
A. Bar chart
B. Pie chart
C. Scatter plot
D. Histogram of residuals
8. What is the benefit of using stratified sampling over simple random sampling in some situations?
A. Stratified sampling is always cheaper.
B. Stratified sampling can reduce sampling error and improve representativeness, especially when subgroups within the population are of interest.
C. Simple random sampling is more complex to implement.
D. Stratified sampling is less prone to bias.
9. Which type of error is considered more serious in many business contexts: Type I or Type II?
A. Type I error is always more serious.
B. Type II error is always more serious.
C. The seriousness depends on the specific business context.
D. Neither type of error is serious in business.
10. In statistics, `variance` measures:
A. The central tendency of data.
B. The spread or dispersion of data points around the mean.
C. The median value of data.
D. The most frequent value in data.
11. In statistics, a `population` refers to:
A. A large group of people
B. The entire set of individuals, items, or data points of interest in a study
C. A subset of data used for analysis
D. The general public
12. What is the purpose of hypothesis testing in business decision-making?
A. To prove a theory is absolutely true
B. To provide evidence to support or reject a claim about a population
C. To calculate descriptive statistics
D. To create data visualizations
13. Which of the following is a potential problem with using convenience sampling?
A. It is too expensive.
B. It may not be representative of the population.
C. It always requires a large sample size.
D. It is difficult to implement.
14. 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
15. What is the primary goal of exploratory data analysis (EDA)?
A. To confirm pre-existing hypotheses.
B. To summarize and describe the main characteristics of a dataset and uncover patterns.
C. To build predictive models.
D. To perform hypothesis testing.
16. Which statistical test is appropriate for comparing the means of two independent groups?
A. Chi-square test
B. Paired t-test
C. Independent samples t-test
D. ANOVA
17. What does a high correlation coefficient (close to +1 or -1) between two variables indicate?
A. A causal relationship between the variables.
B. A strong linear relationship between the variables.
C. No relationship between the variables.
D. A non-linear relationship between the variables.
18. What is the purpose of calculating confidence intervals?
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 sample statistics.
D. To describe the sample data.
19. A company wants to estimate the average income of its customers. Which statistical method is most appropriate?
A. Descriptive statistics and confidence intervals
B. Hypothesis testing for proportions
C. Regression analysis
D. Time series analysis
20. Which statistical method is used to analyze categorical data and examine the association between two or more categorical variables?
A. Regression analysis
B. ANOVA
C. Chi-square test
D. T-test
21. Which of the following is an example of ratio data?
A. Temperature in Celsius
B. Customer`s income in dollars
C. Ranking of employees performance
D. Colors of cars
22. What is the `interquartile range` (IQR)?
A. The range of all data values.
B. The range of the middle 50% of the data.
C. The average of the upper and lower quartiles.
D. The standard deviation multiplied by the sample size.
23. What is the purpose of statistical inference?
A. To describe the sample data.
B. To make generalizations about a population based on sample data.
C. To calculate descriptive statistics.
D. To organize and present data.
24. Which of the following statistical techniques is used to examine the relationship between two quantitative variables?
A. Chi-square test
B. Regression analysis
C. ANOVA
D. T-test
25. In business forecasting, what is the `moving average` technique primarily used for?
A. To identify seasonal patterns in data.
B. To smooth out short-term fluctuations and highlight longer-term trends.
C. To measure the volatility of data.
D. To predict exact future values with high accuracy.
26. What is the difference between a parameter and a statistic?
A. A parameter is calculated from a sample, while a statistic is calculated from a population.
B. A parameter describes a population, while a statistic describes a sample.
C. There is no difference; they are interchangeable terms.
D. A parameter is always known, while a statistic is always unknown.
27. In regression analysis, the R-squared value represents:
A. The slope of the regression line.
B. The intercept of the regression line.
C. The proportion of variance in the dependent variable explained by the independent variable(s).
D. The standard error of the regression model.
28. Which of the following is a limitation of using statistical models in business?
A. Statistical models are always perfectly accurate.
B. Statistical models can only be used for large datasets.
C. Statistical models rely on assumptions that may not always hold true in real-world scenarios.
D. Statistical models eliminate all uncertainty in decision-making.
29. What does a p-value less than the significance level (α) in hypothesis testing indicate?
A. The null hypothesis is likely true.
B. There is strong evidence to reject the null hypothesis.
C. A Type II error has occurred.
D. The sample size is too small.
30. What is the purpose of data cleaning in the statistical analysis process?
A. To make the data look visually appealing.
B. To transform data into different formats.
C. To identify and correct errors, inconsistencies, and missing values in data.
D. To perform statistical calculations.
