BRM Final Exam Multiple Choice (75%) 1. The empirical probability is found by taking the _____a_____ and dividing it by the _____b______. a) a=total number of times experiment is performed, b=total number of outcomes b) a=total number of outcomes, b=total number of times experiment is performed. c) a=total number of times successes appear, b=total number of outcomes d) a=total number of times successes appear, b=total number of times experiment is performed e) a=number of ways to get a particular outcome, b=total number of outcomes. 2. It is possible for two variables to be causally linked but still have low correlation. a) True b) False 3. A \"95% Confidence Interval\" can be interpreted as the probability that that population parameter is not in the interval found. a) True b) False 4. One way to interpret the slope of the regression line is to view it as the initial value of the response variable when the explanatory variable is set equal to 0. a) True b) False 5. Prediction of a particular value of a response variable by providing an explanatory variable can be done after a regression by a) Using the statistical significance and confidence intervals b) Using the R^2 of the regression c) Using the equation of the line found by the slope and intercept d) Using the equation of the line found by the significants and the error terms e) None of the above 6. The empirical probability will exactly equal the analytical probability (assuming one exists) when an experiment is performed a) A small number of times. b) A large number of times but still finite (meaning, an actual number, but just a really big number). c) An infinite number of times d) A negatively infinite number of times. e) None of the above. 7. In a scatter plot, a positive linear trend is when a) The data for the response variable is increasing as the data in the explanatory variable's is increasing. b) The data for the response variable is decreasing as the data in the explanatory variable's is increasing. c) The data for the response variable is increasing as the data in the explanatory variable's is decreasing. d) The data is spread far apart from each other e) The data is clustered closer to each other. 8. Bill decides to toss a coin to see if it is \"fair\". He tosses it 105 times and counts how many times heads appears. He counted 34 times. The empirical probability of the coin showing up on \"heads\" is: a) .5 b) .43333 c) .34 d) .324 e) .234 9. Jill wants to throw two dice. Each die has 7 sides, labeled from 1 - 7. Assuming each side is equally likely, what is Jill's probability of rolling either an even number or an odd number? a) .2 b) 0 c) .3 d) 1 e) 5 10. Which interval would represent a 100% confidence interval of a number who's true parameter is 45.5? a) [45,55] b) [35,65] c) [25,75] d) It's impossible to get a 100% confidence interval. e) (-,+) 11. For a mean, the way in which we find the confidence interval is by taking the statistic found from our data and adding it to the standard deviation. a) True b) False 12. A researcher notices that her data in her scatterplot is trending from lower to higher as she moves from left to right. She also notices that most of the data points are clustered together on this trend. If she were to run a correlation, she would most likely find that a) The correlation will be close to -1 b) The correlation will be close to 1 c) The correlation will be close to 0 d) There is not enough information to say. e) None of the above 13. In a survey bias can result from a) how the sample was chosen. b) how the survey question was worded. c) Both A and B are correct. d) None of the above 14. In order to create groups of subjects that should be similar, on average, in all respects, we use a) lurking. b) confounding. c) randomization. d) All of the above Below is a histogram of the ages of the professors at a large university. 15. The overall shape of this distribution is a) skewed to the right b) skewed to the left c) roughly symmetric d) without a clear shape 16. A convenience sample is one taken at a a) convenience store b) convenient time c) convenient place d) B) or C) 17. A simple random sample of size 1600 is taken. The margin of error is a) 0.01 b) 0.10 c) 0.025 d) 0.05 A student's research shows that there were more suicides in 2010 than there were in 1910. He concludes that people were less likely to commit suicide in 1910 than in 2010. 18. Why is it not valid to use these two numbers to compare suicides in these two years? a) People were happier in 2010 than they were in 1910. b) The numbers were compiled by a student instead of by a professional researcher. c) The U.S. population increased substantially from 1910 to 2010. d) One shouldn't compare years that are so far apart. 19. What would be a more appropriate or valid measure for this comparison? a) Compare the number of suicides in 1900 and 2000. b) Compare the suicide rates (percentages) for 1910 and 2010. c) Compare the number of suicides in those years, grouped by region. d) Compare the number of people who don't commit suicide for 1910 and 2010. 20. A 95% confidence interval for a company's profit is ($3,250,000,$3,750,000). This means that a) 95% of the company's profit is between $3,250,000 and $3,750,000. b) 95% of the company's accountants believe that the company's profit is between $3,250,00 and $3,750,000. c) A) and B). d) none of the above. 21. A company's accountants figure out that next year, a company's profits will be $3,000,000 with probability 0.25, $4,000,000 with probability 0.60, and $5,000,000 with probability 0.15. The expected profit for next year is a) impossible to calculate without further information. b) $4,000,000 c) $3,900,000 d) $12,900,000 22. In the regression on the right, which is the correct formula for the average income (i) when a height (h) is given? a) i=2936.18 b) i=5215.48h c) i=2936.18h d) i=2936.18h+5215.48 e) i=5215.48h+2936.18 f) i=5215.48 23. Is the \"height\" variable significant? a) Yes b) No 24. Does the output suggest that the equation fits the data well? a) Yes b) No 25. FREEBIE! (3 Points!) Open Ended(25%) 1.) (12.5 pts) Bob wants to play a casino game where there are only two outcomes: win or loose. If Bob wins, he is able to keep his original bet of $4 but in addition to this gains $10. If Bob looses, then he looses his bet of $4. What is the expected winnings Bob can expect to see, on average per game played, if the probability of loosing is 2/3 and the probability of winning is 1/3? SHOW ALL OF YOUR WORK! 2.) (12.5 pts) Give a good and logical reason as to why correlation does not imply causation. Explain in full. Maximum ONE paragraph