Midterm 2 Study Guide

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Statistics

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Feb 20, 2024

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Stat 100 Fall 2023 Midterm Exam #2 Study Guide Instructions Questions on Midterm Exam #2 covers content from Chapters 11 - 24. The exam questions focus on your conceptual understanding. All questions are multiple choice, and there is only one correct answer for each question. All questions relating to computations can be answered by using your intuition and conceptual understanding of the statistics in question, however you are allowed the use of a calculator if you choose. You are expected to answer the questions in a manner consistent with the University of Illinois's policies relating to academic integrity. You must answer all questions individually without the help of any other person. This is a closed book exam. You are allowed one single-sided 8.5x11 page of notes. The exam contains 40 questions. All questions are worth 1 pt. You are allowed 90 minutes to complete the exam. To help you answer questions, a graphic of the empirical rule is included. This is the last page of your exam - you may tear it off now if you would like. This exam will test your knowledge in: - (~15%) interpreting data presented in a two-way (a.k.a. contingency) table - identifying row proportions and column proportions - applying concepts such as independence, dependence, mutual exclusivity, joint and disjoint probabilities - (~25%) understanding the central limit theorem - identifying expected values and standard errors from box models - evaluating the relationship between sample size, standard deviation, and standard error - (~25%) utilizing the principles of study design to evaluate data - applying concepts such as random assignment, similarity between control and treatment groups, random sampling, and representativeness of a sample - identifying potential confounding bias, questionnaire bias, non-response bias, and coverage bias - (~10%) understanding the principles of estimation - applying concepts such as confidence level and margin of error - creating 95% confidence interval estimates - (~15%) applying the principles of hypothesis testing - identifying hypotheses and their associated probability distributions - interpreting p -values and contextualizing statistical results - conducting a one-sample Z test, and a chi-squared test - understanding the different uses for a Z-test, a T-test, and a Chi-Squared test Included in this study guide is a list of questions regarding key concepts, definitions, and terms.
Use the following table to answer questions 1-4. Stat 100 Section by Year-in-School 1st Year Not 1st Year Total Prof Rao’s Section 700 300 1000 Prof Clement’s Section 100 100 200 Total 800 400 1200 1. If Professor Rao and Professor Clement randomly pick one student from Stat 100, what is the probability that they are in Professor Rao’s section given that they are a 1st year? a. 66.7% b. 70.0% c. 83.3% d. 87.5% 2. What proportion of Professor Clement’s students are 1st years? a. 12.5% b. 16.6% c. 25% d. 50% 3. Professor Clement and Professor Rao are interesting in knowing if a student’s year-in-school is related to which Stat 100 section the student is in. They decide to conduct a chi-squared test for independence. What is the expected count for the number of 1st year students in Professor Rao’s section? a. 500 b. 666 c. 833 d. 1000 4. The expected count for the number of not-first-year students in Professor Clement’s section is 33. What is the contribution to the chi-squared test statistic for this cell? a. 67 b. 2 c. 136 d. 4
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Every Saturday morning, Professor Rao goes for a walk near a pond and counts how many ducks and geese he sees. Over this past semester, he has taken 16 such walks. On average, he sees 20 ducks and geese on a single walk, with a standard deviation of 4. Use this information to answer questions 5-8. 5. Next fall, Professor Clement is interested in joining Professor Rao on these walks. If they were to take 16 walks together, how many total ducks and geese do they expect to see? a. 20 b. 80 c. 320 d. 400 6. What is the standard error for the total number of ducks they might see next fall? a. 1 b. 4 c. 16 d. 64 7. Suppose that they end up seeing a total of 336 ducks and geese. What is the z-score for this observed value? a. -4 b. 1 c. 4 d. 16 8. What is the p -value comparing this observation to their expectations? a. p < .001 b. p = .025 c. p = .135 d. p = .16
The company Research Co. has conducted a survey to ascertain Canadians’ attitudes towards education. Here is there sampling methodology: Methodology: Results are based on an online study conducted from October 20 to October 22, 2023, among 1,000 adults in Canada. The data has been statistically weighted according to Canadian census figures for age, gender and region. The 95% confidence level margin of error – which measures sample variability – is +/- 3 percentage points. 9. Professor Clement and Professor Rao hire Research Co. to re-conduct the study, but they want the company to produce a margin of error of only 1 percentage point. How large of a sample should the company recruit? a. 111 adults in Canada b. 333 adults in Canada c. 3000 adults in Canada d. 9000 adults in Canada 10. By stating that “the data has been statistically weighted according to Canadian census figures for age, gender, and region”, Research Co. is stating that they used a method called “raking”. This is similar to the idea of quota sampling. Quota sampling as a sampling strategy is most concerning in terms of its implications for a. confounding bias b. coverage bias c. response bias d. questionnaire bias
Appendix A - Empirical Rule
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Key definitions and terms from Chapters 11 - 24 Chapters 11-12 What is the probability of an outcome? What is independence, for two events? What is dependence, for two events? What is conditional probability? What is mutual exclusivity? What does it mean if two events are disjoint? Chapters 13-16 What is a box models? What is a random variable? What does the distribution generated by enacting simulation with a box models represents? What is the expected value of the sum of n draws from a box? What is the standard error of the sum of n draws from a box? What is the expected value of the average of n draws from a box? What is the standard error of the average of n draws from a box? What is the square root law? What is the central limit theorem? Chapters 1, 2, and 17 What is an experiment? What is the purpose of a control group? Why should control groups by as much like the treatment group as possible? What is blocking? Why is random assignment important? What is confounding bias? What is post-stratification? What is a target population? What is a sample? What is an inference?
What are the two types of inferences we discussed this semester? What is a population parameter? What is a sample statistic? Why is representativeness of a sample important? What is quota sampling? What is self-selected sampling? What is probability sampling? Why is probability sampling important? What is non-response bias? What is questionnaire bias? What is coverage bias? Chapters 18-19 What is a confidence interval? What does the standard error describe? What does the standard deviation describe? What is a margin of error? How is sample size related to margin of error? What is a confidence level? How is confidence level related to margin of error? How is standard deviation related to margin of error? Chapters 20-21 and 23-24 What is the purpose of a hypothesis test? What makes a hypothesis a statistical hypothesis? What is a p -value? What guidelines do we use to interpret p -values? When should we use a T test, instead of a Z test? What is the difference between a T distribution and a Z distribution? When should we use a chi-squared test?
How does a chi-squared test turn an entire sample into a single number? What is the equation for the contribution of a cell to the chi-squared test statistic? What is the main hypothesis that allows us to compute expected counts in a chi-squared test for independence? What is practical significance? Why is it possible to get a small p -value even if the statistical hypothesis being tested is correct? What is the most important thing to remember from this class?
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