Midterm Exam Practice Problems CHAPTER 4: The Normal Distribution 1. List the properties of the normal distribution Scores on the Math Section of the GRE are normally distributed with a mean of 520 and a standard deviation of 15. [Use the basic properties of the Normal Distribution and a ZScore Tabiel 2. Half of the scores are higher than 3. What percentage of test takers score higher than 535? _ 4. What percentage of test takers score lower than 505? _ _ 5. What percentage of test takers score higher than 500? Among WSSU faculty, commute time is normally distributed with a mean of 25 minutes and a standard deviation of 5 minutes 6. What percentage of faculty have a commute time that is higher than average? 7. What percent of faculty spend more than 32 minutes commuting to work? 8. What percent of faculty spend less than 37 minutes commuting to work? 9. Do you think commute time for the entire student population is also normally distributed? Why or why not? 10. What is the median commute time for faculty members? 2 CHAPTER 5 & CHAPTER 6: Sampling, Sampling Distributions and Estimation CI = Y +Z (x) CI = p+z*, p(1 - p) 11. What is the CLT (Central Limit Theorem)? State in your own words N 12. What is a good estimate of the minimum number of samples to be able to use Central Limit Theorem? 13. If there are 10 M&Ms - 4 blue, 2 red, 2 green, and 2 brown is the probability of picking a green M&M? 14. If you wanted to eat half of the M&Ms and still keep the same probabilities as when you had 10, how many blue M&Ms would be left? 15. How does the standard deviation of the sampling distribution [AKA the standard error] change as the sample size increases? 16. If the population mean is 100, and the sample size is only 300, what will be the mean of the sampling distribution? 17. You want to know the average amount of money that Americans spend, out of pocket, on health care costs per year. Do you think the distribution of money spent out of pocket on health care costs is normally distributed? Why or Why Not?18. You collect a sample of 1296 individuals. The sample mean is $450 and the sample standard deviation is $137. Calculate a 95% Confidence Interval for the amount of money that Americans spend out of pocket on health care costs per yea r. ______ 19. Calculate a 99% Confidence Interval for the amount of money that Americans spend out of pocket on health care costs per yea r. 20. lfyou were to calculate a 90% Confidence Interval, would it be wider or more narrow than the 95% Confidence Interval?? 21. You want to know the population mean of the number of hours of television watched per week in households across the US. You collect a sample of 410 households, and find that the sample mean is 19 hours, with a standard deviation of 3.46 hours. Calculate the 95% confidence 22. A sample of 1000 Americans reveals that 10% have experienced homelessness at some point in their life. You want to estimate with 90% confidence the population's experience of homelessness. Calculate the 90% confidence interval. CHAPTER 7: Hypothesis Testing 23. Given the following research question, state the null and research/alternative hypotheses. Ford is testing the fuel efficiency of their vehicles using regular gasoline and an ethanol mix. They wonder if vehicles that get the ethanol mix are less fuel efficient than vehicles which use gasoline. a. Null (.5 pts) _______ b. Research/Alternative Hypothesis (.5 pts) c. One Tail or Two Tail test? 24. You want to know if earning a college degree has any impact on earnings for non-traditional students (age 40+). a. What is the null hypothesis? _ _ _ b. What is the research/alternative hypothesis? c. One Tail or Two Tail test