Presentation on theme: "Warm-up Ch. 7 Practice Test"— Presentation transcript:
1 Warm-up Ch. 7 Practice Test In the late 1990’s the Bill and Melinda Gates Foundation began funding an effort to encourage the breakup of large schools into smaller schools. Why? It had been noticed that smaller schools were more common among best-performing schools than one would expect. In time many other organizations and the U.S. Department of Education’s Smaller Learning Communities Program supported the effort. Well over a billion dollars was spent making schools smaller. Two statisticians discovered that in one particular state 12% of the top scoring schools were the smallest 3% BUT also 18% of the lowest scoring schools were also the smallest. Explain why small schools show up at both extremes.
4 Example 2Drivers in the Northeast and Mid-Atlantic states had the highest failure rate, 20%,on the GMAC Insurance National Driver’s Test. (They also were the drivers most likely to speed.) Describe the shape, center, and spread of the sampling distribution of the proportion of drivers. Who would fail the test in a random sample of 60 drivers from these states. What are the reasonably likely proportions of drivers who would fail the test?
5 Whiteboard Review1. Five math teachers are asked how many pens theyare currently carrying, and the results are 1, 1, 1, 2, 2.Random samples of size two are taken from this population(without replacement). What is the median of the samplingdistribution of the median?11.41.52None of the Above
6 Question 2) Whiteboard Review Two antidepressants are to be compared in the treatment of elderly patients in a nursing home. Each patient has his or her own room, some with spectacular views of the ocean. The experimental design is to create homogenous blocks with respect to the window view. How should randomization be used for a randomized block design?Within each block, randomly pick half of the patients to receiveeach antidepressant.B. Randomly pick half of all patients to receive each antidepressant, butthen analyze the results separately by blocks.C. Randomly choose which blocks will receive which antidepressant.D. Randomly choose half the blocks to receive each antidepressant for agiven time period; then for the same time period switch the medicationin each block and compare the results.E. For ethical reasons, allow patients to choose which medication theyprefer taking, but then randomly assign patients to blocks.
7 Question 3) Whiteboard Review There are two games involving flipping a fair coin. In the firstgame, you win a prize if you can throw between 45% and 55%heads; in the second game, you win if you can throw morethan 60% heads. For each game, would you rather flip thecoin 30 times or 300 times?30 times for each game.300 times for each game30 times for the first game, 300 for the second300 times for the first game, 30 for the secondThe outcomes of the game do not depend on the numberof flips.
8 Question 4) Whiteboard Review Which of the following statements are true?Both dotplots and stemplots can show symmetry, gaps, clusters and outliers.In histograms, relative areas correspond to relative frequencies.In histograms, frequencies can be determined from relative heights.A. II only B. I and II C. I and III D. II and III E. I, II and III
9 Question 5) Whiteboard Review The scores on a standardized test are normally distributedwith mean 500 and standard deviation 110. In a randomlyselected group of 100 test-takers, what is the probabilitythat the mean test score is above 510?Less than0.18170.46380.53620.8183
10 Question 6) Whiteboard Review Last Bonus Question On an average day in 2004, about 246,000 vehicles traveledeast on the Santa Monica freeway in Los Angeles to theInterchange with the San Diego freeway. Assume thata randomly selected vehicle is equally likely to go straightthrough the interchange, go south on the San Diego freeway,or go north on the San Diego freeway. What is the best estimate of the number of vehicles that will go straight through the interchange on an average day?b. What numbers of vehicles are reasonably likely to go straight through?
11 Directions to Ch. 7 Review Complete the Ch. 7 ReviewThe test is not until Monday March 5thWe will review the Multiple Choice today and the free response next blockNext block we will start on Ch. 8Have your notebooks readyVocabulary: sampling distribution, standard error, reasonably likely,rare events, standard error of the mean, Central Limit Theorem(6 for 2 pts each = 12 pts) Formulas: S.E. and S.E. of the mean ( 4pts)Notes with Warm-ups: 7.1, 7.2, 7.1 and 7.2 Review, 7.3( 4 for 21 pts each; 15 for notes and 6 for warm-up = 84 pts)
12 Mistakes from the last quiz Human gestation (pregnancy) times have a mean of about 266 days, with a standard deviation of about 16 days. 1. Suppose we look at the average gestation time for a sample of 100 women. If we imagined all the possible random samples of 100, what would the distribution look like? Draw it below. 2. Label the center and the two standard errors of the mean on either side of the center in your distribution diagram above.
13 3 ConditionsRandomization – It didn’t say anywhere the police randomly selected cars, but you had to mention why or why not there was randomization. 10% - 80 cars is definitely less than 10% of all the cards on the major highway. Success/failure- 70% of 80 cars is 56 cars that should be speeding which is more than % of 80 is also greater than 10. There is enough in the sample to have more than 10 in each of the categories of speeding or not speeding.
14 Answers to Multiple Choice 1) C 2) B 3) A 4) C 5) B