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**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.

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7.3 E #35

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7.3 E #40

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Example 2 Drivers 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?

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Whiteboard Review 1. Five math teachers are asked how many pens they are 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 sampling distribution of the median? 1 1.4 1.5 2 None of the Above

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**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 receive each antidepressant. B. Randomly pick half of all patients to receive each antidepressant, but then 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 a given time period; then for the same time period switch the medication in each block and compare the results. E. For ethical reasons, allow patients to choose which medication they prefer taking, but then randomly assign patients to blocks.

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**Question 3) Whiteboard Review**

There are two games involving flipping a fair coin. In the first game, you win a prize if you can throw between 45% and 55% heads; in the second game, you win if you can throw more than 60% heads. For each game, would you rather flip the coin 30 times or 300 times? 30 times for each game. 300 times for each game 30 times for the first game, 300 for the second 300 times for the first game, 30 for the second The outcomes of the game do not depend on the number of flips.

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**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

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**Question 5) Whiteboard Review**

The scores on a standardized test are normally distributed with mean 500 and standard deviation 110. In a randomly selected group of 100 test-takers, what is the probability that the mean test score is above 510? Less than 0.1817 0.4638 0.5362 0.8183

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**Question 6) Whiteboard Review Last Bonus Question**

On an average day in 2004, about 246,000 vehicles traveled east on the Santa Monica freeway in Los Angeles to the Interchange with the San Diego freeway. Assume that a randomly selected vehicle is equally likely to go straight through 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?

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**Directions to Ch. 7 Review**

Complete the Ch. 7 Review The test is not until Monday March 5th We will review the Multiple Choice today and the free response next block Next block we will start on Ch. 8 Have your notebooks ready Vocabulary: 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)

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**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.

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3 Conditions Randomization – 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.

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**Answers to Multiple Choice**

1) C 2) B 3) A 4) C 5) B

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