Probability and Statistics

True or False Instructions: If the statement is true, say so. If it is false, either: a. State the corrected statement b. Provide a counter example c. Say why the statement is incorrect. 1. If the 95% confidence interval for the slope of the true regression line is (-1.44,0.199). The estimate for is significantly different from 0. 2. Correlation implies causation. 3. A correlation coefficient of r = 0.1 implies that there is no relationship between the variables 4. A 99% confidence interval of (0,1) is interpreted as being 99% confident that the true parameter value is in the range from 0 to 1. 5. When counting, a combination implies that order doesn’t matter. Hence, if a class of 25 elects 3 persons to fill the positions president, treasurer and secretary, then a combination can be used to count the number of ways this group can be formed. 6. If A and B are independent, then P(A|B)=P(B) 7. If I roll 2 dice where the event A= getting a 6 on dice 1 and event B is getting a 3 on dice 2. Events A and B are not independent. 8. The central limit theorem states that if the sample size is large enough, then each sample is normally distributed. 9. Failing to reject the null hypothesis in any hypothesis test means that the null hypothesis is true. 10. Power is the probability of rejecting the null hypothesis when the null hypothesis is not true 11. As the distance between the null mean and the true mean decreases, the power increases. 12. A simple random sample is not truly random. 13. There are 2 methods we learnt in this class to make inference: Hypothesis testing and Confidence intervals. We use a Hypothesis test when we have prior information about the population. 14. To find an MVUE, we find the estimator that is unbiased, has minimum variance and is in the lower percentile. Multiple Choice Instructions: Provide some justification as to why you chose a specific answer. 15. Which of the following statements are not correct? a) The coefficient of determination, denoted by is interpreted as the proportion of observed y variation that cannot be explained by the simple linear regression model. b) The higher the value of the coefficient of determination, the more successful is the simple linear regression model in explaining y variation. c) If the coefficient of determination is small, an analyst will usually want to search for an alternative model (either a nonlinear model or a multiple regression model that involves more than a single independent variable). d) All of the above statements are correct. 16. In testing t check this probability? a) Geometric distribution b) Binomial Distribution c) Hypergeometric distribution d) Poisson distribution e) None of the above 20. A sample a) is a small amount of a food or other commodity, especially one given to a prospective customer b) is a subset of the population c) means that population is unbiased d) might increase the probability that a customer will buy a product. e) is the part of the population that is not selected Answer Key NAME:_________________________ STUDENT ID:_____________________________ Academic Integrity Statement All students must sign the following Academic Integrity statement before submitting the exam: For this exam, I acknowledge that I have followed all the above instructions for the exam. I understand that acts of academic dishonesty may result in penalty up to the full extent allowed by Washington State University Academic Integrity Policy. 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