Math 140E: Test #3 Fall 2008 Page 1 of 6 Your Name: _________________________ Math 140: Statistics Test 3, November 20, 2008 1. (4 pts) Match the formula in the first column with the description in the second. Put your answer in the blank provided in the second column. i) € numberDraws × SD a) SE for Average: _____ ii) € numberDraws × SDnumberDraws b) Combined SE _____ iii) € numberDraws × SDnumberDraws×100 c) SE for Percent: _____ iv) € 1stSE2+ 2ndSE2 d) SE for Sum: _____ 2. (5 pts.) Prior to the election, one hundred voters were asked for whom they planned to vote in order to estimate the outcome of the election. Identify each of the following using the language from the Introduction to Chapter 19. a) The 100 voted that were interviewed: _______________ b) All voters on election day: _______________ c) The percentage of all voters voting for a particular candidate: _______________ d) The percentage of those interviewed voting for a particular candidate: _______________ e) The process of drawing a conclusion about the outcome of the election: _______________ 3. (2 pts.) True or False: When a selection procedure is biased, taking a larger sample will help. _______________ 4. (2 pts.) True or False: With a simple random sample, all possible samples are equally likely to be drawn. _______________Math 140E: Test #3 Fall 2008 Page 2 of 6 5. (12 pts.) In a hypothetical city with a population of 100,000 eligible voters, 82,000 plan to vote in the next election. A sample of 6400 people is drawn without replacement. a) Find the expected value and SE for the number of people in the sample that plan to vote. b) Find the percentage and percent SE of people planning to vote. c) Estimate the chance that between 80% and 82% of the people in the sample plan to vote. d) Find the correction factor and the corrected percent SE.Math 140E: Test #3 Fall 2008 Page 3 of 6 6. (15 pts.) Drawing 900 tickets, with replacement, from a box, 320 were red and the rest were black. a) Estimate the standard deviation of the box. b) Estimate the percentage of red tickets in the box as a give or take number. c) Construct a 95% confidence interval for the experiment. d) Construct an 80% confidence interval for the experiment. e) If 400 draws are made gives the same fraction of red cards how does the 95% confidence interval change? Give a number. 7. (8 pts.) For 1000 random draws made from a box with replacement, a red card was drawn 48% of the time. Someone claims that half the cards in the box are red. What do you conclude?Math 140E: Test #3 Fall 2008 Page 4 of 6 8. (18 pts.) A gambler asserts that a die is biased, that it lands showing a six too often. She rolls the die 100 times and it lands on a six 22 times. a) Give a box model for the experiment. b) Briefly state the null and alternative hypothesis. c) Based on the null hypothesis, what is the expected value for 100 rolls of the die? d) Estimate the SD and appropriate SE. e) Calculate the z-statistic for the experiment. f) Calculate the P-value for the experiment. What do you conclude?Math 140E: Test #3 Fall 2008 Page 5 of 6 9. (16 pts.) Seventy-five draws from box A have an average of 78 and an SD of 14. Fifty draws made from box B have an average of 79 and an SD of 15. All draws are random draws with replacement. a) What is the appropriate SE for Box A? b) What is the appropriate SE for Box B? c) What is the combined SE for the two boxes? d) Estimate the difference of the averages of the two boxes as a give-or-take number.Math 140E: Test #3 Fall 2008 Page 6 of 6 10. (18 pts.) In a marketing test of a new breakfast cereal, 1000 families were divided into two groups of 500 each. One group was given the new improved corn flakes while the others were given the current version of the cereal. Those receiving the new cereal are an average of 5.2 bowls of the cereal each week with a SD of 1.5 bowls. Those given the original flavored cereal ate 4.9 bowls of cereal each week with an SD of 2.2 bowls. a) Formulate the null and alternative hypotheses. b) What is the appropriate SE’s for the experimental treatment and the standard treatment? c) What is the combined SE for the study. d) Calculate the z-value and P-value. e) Is the difference in cereal consumption statistically significant? Highly significant? f) What conclusion would you reach? Pledged: