(JHU) EN.553.111 Statistical Analysis I Final Exam Review Q & S 2024, Exams of Economics

Download (JHU) EN.553.111 Statistical Analysis I Final Exam Review Q & S 2024 and more Exams Economics in PDF only on Docsity! EN.553.111 Statistical Analysis I Final Exam Review Q & S 2024 1. Multiple Choice: Which of the following is a measure of central tendency? a) Variance b) Skewness c) Median d) Range Correct Answer: c) Median Rationale: The median is a measure of central tendency, which indicates the middle value of a data set when it is ordered from least to greatest. 2. True/False: The mode is the most frequent value in a data set. Answer: True Rationale: The mode refers to the most frequently occurring value in a data set, which is a concept in descriptive statistics. 3. Fill-in-the-Blank: In probability theory, an event that cannot occur simultaneously with another event is called __________. Correct Answer: Mutually exclusive Rationale: Mutually exclusive events are those that cannot occur at the same time, which is a fundamental concept in introductory probability. 10. Multiple Choice: Hypothesis testing is used to determine: a) If the data fits the model b) If the model fits the data c) If the sample data is consistent with a hypothesis about the population d) The probability that the model is correct Correct Answer: c) If the sample data is consistent with a hypothesis about the population Rationale: Hypothesis testing is a method of statistical inference used to decide whether the sample data is consistent with a stated hypothesis. 11. True/False: The p-value is the probability that the null hypothesis is true. Answer: False Rationale: The p-value is the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is true. 12. Fill-in-the-Blank: In classical estimation, the __________ estimator is the one that has the smallest variance among all unbiased estimators. Correct Answer: Efficient Rationale: An efficient estimator is one that achieves the lowest possible variance among all unbiased estimators of a parameter, minimizing the error. 13. Multiple Choice: Which of the following is not a property of a good estimator? a) Unbiasedness b) Efficiency c) Consistency d) Complexity Correct Answer: d) Complexity Rationale: Complexity is not considered a property of a good estimator in statistics. The properties of a good estimator typically include unbiasedness, efficiency, and consistency. 14. True/False: Sampling error decreases as the sample size increases. Answer: True Rationale: Sampling error tends to decrease as the sample size increases due to the Law of Large Numbers, which states that larger samples are more representative of the population. Multiple Choice: Question: What does the central limit theorem state? A. The mean of the sampling distribution is equal to the population mean. B. The shape of the sampling distribution is always skewed. C. The sampling distribution of the sample mean approaches a normal distribution as the sample size increases. D. Variance of the sampling distribution decreases as the sample size decreases. Correct Answer: C Rationale: The central limit theorem asserts that the sampling distribution of the sample mean becomes approximately normal regardless of the shape of the population distribution as the sample size increases. Fill-in-the-Blank: Question: The process of drawing conclusions about a population based on a sample is known as _. Correct Answer: Inference Rationale: Inference involves using sample data to make generalizations or predictions about a larger population. True/False: Question: Confidence intervals provide a range of values within which the true population parameter lies. Correct Answer: True Rationale: Confidence intervals estimate the range within which a population parameter is likely to fall. Multiple Choice: Multiple Choice: Question: Which of the following is a measure of central tendency? A. Standard deviation B. Interquartile range C. Mean D. Variance Correct Answer: C Rationale: The mean is a measure of central tendency that represents the average value of a dataset. Fill-in-the-Blank: Question: Robust estimation methods are resistant to the influence of _ in the data. Correct Answer: Outliers Rationale: Robust estimation techniques are designed to minimize the impact of outliers on statistical analyses. True/False: Question: Sampling error arises due to differences between a sample and the entire population. Correct Answer: True Rationale: Sampling error occurs when the characteristics of a sample differ from those of the entire population, leading to inaccuracies in estimates. Multiple Choice: Question: Which statistical concept involves making decisions based on sample data to assess the validity of a hypothesis about a population parameter? A. Confidence intervals B. Hypothesis testing C. Random variables D. Central limit theorem Correct Answer: B Rationale: Hypothesis testing is a statistical method used to evaluate hypotheses about population parameters based on sample data. Fill-in-the-Blank: Question: _ statistics summarize the main features of a dataset, such as measures of central tendency and dispersion. Correct Answer: Descriptive Rationale: Descriptive statistics provide insights into the characteristics of a dataset without making inferences about a larger population. True/False: Question: Confidence levels in confidence intervals indicate the probability that the true population parameter falls within the interval. Correct Answer: False Rationale: Confidence levels represent the proportion of confidence intervals that would contain the true population parameter if the sampling process were repeated multiple times. **1. Which measure of central tendency is most affected by extreme values?** a) Mean b) Median c) Mode d) Interquartile range **Answer:** a) Mean *Rationale:* The mean is calculated by summing all the values and dividing by the number of values, so it is more affected by extremely high or low values compared to the median or mode. *Rationale:* Conditional probability quantifies the probability of one event occurring in the presence of another event. **5. A ________ interval provides a range of values within which there is a specified probability that the parameter lies.** **Answer:** Confidence *Rationale:* A confidence interval gives an estimated range believed to contain the parameter with a certain level of confidence, typically 95% or 99%. **6. The law of large ________ states that as the number of trials increases, the empirical probability of an event converges to the theoretical probability of the event.** **Answer:** Numbers *Rationale:* The law of large numbers indicates that large sample sizes yield probabilities that get closer to the expected value. ### True/False Questions **7. The median is unaffected by the presence of outliers in a dataset.** **Answer:** True *Rationale:* The median, as the middle value of a dataset, is not affected by extreme outliers like the mean is. **8. In hypothesis testing, a Type I error is rejecting the null hypothesis when it is in fact true.** **Answer:** True *Rationale:* A Type I error occurs when we reject a true null hypothesis, often referred to as a "false positive." **9. The expectation of a random variable is the weighted average of all possible values that this random variable can take on.** **Answer:** True *Rationale:* Expectation reflects the average expected value based on the probabilities of all possible outcomes. ### Advanced Concept Questions #### Multiple Choice **10. In descriptive statistics, which of the following best describes the skewness of a distribution?** a) It measures the spread of the data. b) It measures the symmetry of the data distribution. c) It measures the central tendency of the data. d) It measures the relationship between two variables. **Answer:** b) It measures the symmetry of the data distribution. *Rationale:* Skewness quantifies the degree of asymmetry of a distribution around its mean. **11. If a die is rolled twice, what is the probability of getting two sixes (assuming each roll is independent)?** **Answer:** Null *Rationale:* The null hypothesis asserts that any observed effect is due to sampling or experimental error. **15. Under simple random sampling, every individual in the population has an ________ chance of being selected.** **Answer:** Equal *Rationale:* Simple random sampling ensures every individual has the same probability of being chosen. #### True/False **16. The confidence level of a confidence interval increases as the width of the interval decreases.** **Answer:** False *Rationale:* Generally, the confidence level and interval width move in opposite directions; a higher confidence level leads to a wider interval. **17. The sum of the probabilities of all mutually exclusive outcomes of a random experiment is always one.** **Answer:** True *Rationale:* Probabilities of all possible outcomes in a probability space must sum to one. **18. In a right-skewed distribution, the mean is typically greater than the median.** **Answer:** True *Rationale:* For right-skewed distributions, the tail on the right side pulls the mean to be higher than the median. #### Multiple Choice **19. Which of the following statements about the p-value in hypothesis testing is correct?** a) It is the probability of not getting the observed data under the null hypothesis. b) It measures the strength of the evidence against the null hypothesis. c) It is the threshold for rejecting the null hypothesis. d) It is always equal to the significance level. **Answer:** b) It measures the strength of the evidence against the null hypothesis. *Rationale:* The p-value represents the probability of obtaining the observed data, or more extreme, assuming the null hypothesis is true. **20. Which method is commonly used in robust estimation to minimize the influence of outliers?** a) Maximum likelihood estimation b) Method of moments c) Least squares estimation *Rationale:* The correlation coefficient \( r \) quantifies the degree of linear relationship between two variables and ranges between -1 and 1. #### True/False **25. The central limit theorem applies only when the sample size is less than 30.** **Answer:** False *Rationale:* The central limit theorem becomes more applicable as the sample size increases, not decreases, commonly recommended to be 30 or more. **26. A p-value greater than the significance level indicates strong evidence against the null hypothesis.** **Answer:** False *Rationale:* A p-value greater than the significance level means there is not enough evidence to reject the null hypothesis. **27. The cumulative distribution function (CDF) of a random variable gives the probability that the variable takes on a value less than or equal to a specific value.** **Answer:** True *Rationale:* The CDF sums the probabilities of all values up to a given point, providing the total probability that the variable is below or at that point. #### Multiple Choice **28. In an independent sampling distribution, the standard error of the mean decreases when:** a) The sample size increases. b) The sample size decreases. c) The population standard deviation increases. d) The population mean increases. **Answer:** a) The sample size increases. *Rationale:* The standard error of the mean (\(\sigma/\sqrt{n}\)) decreases as the sample size (n) increases, assuming the population standard deviation (\(\sigma\)) remains constant. **29. Which measure indicates the degree of uncertainty or certainty in confidence intervals?** a) Confidence coefficient b) Margin of error c) Sample mean d) Population mean **Answer:** b) Margin of error *Rationale:* The margin of error represents the range above and below the sample statistic within which the population parameter is expected to fall with a given level of confidence.