ch11 - Chapter 11 Solutions 11.1. Both 283 and 311 pushes...

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Chapter 11 Solutions 11.1. Both 283 and 311 pushes per minute are statistics (related to one sample: the subjects with placebo, and the same subjects with caffeine). 11.2. 41% and 37% are parameters (related to the population of all registered voters in Florida); 33% is a statistic (related to the sample of registered voters among those called). 11.3. Both 82% and 18% are statistics, related to those projectile points found at the North Carolina site. (This assumes that we can view those points as a sample from some population—either the population of all points buried at that site, or all points buried in North America.) 11.4. Sketches will vary; one result is shown on the right. 11.5. Although the probability of having to pay for a total loss for 1 or more of the 12 policies is very small, if this were to happen, it would be ±nancially disastrous. On the other hand, for thousands of policies, the law of large numbers says that the average claim on many policies will be close to the mean, so the insurance company can be assured that the premiums they collect will (almost certainly) cover the claims. 11.6. (a) The population is the 12,000 students; the population distribution (Normal with mean 7.11 minutes and standard deviation 0.74 minute) describes the time it takes a randomly selected individual to run a mile. (b) The sampling distribution (Normal with mean 7.11 minutes and standard deviation 0.074 minute) describes the average mile-time for 100 randomly selected students. 11.7. (a) µ = 694 / 10 = 69 . 4. (b) The table on the following page shows the results for line 116. Note that we need to choose 5 digits, because the digit 4 appears twice. (When choosing an SRS, no student should be chosen more than once.) (c) The results for the other lines are in the table; the histogram is shown on the right on the following page. (Students might choose different intervals than those shown here.) The center of the histogram is a bit lower than 69.4 (it is closer to about 67), but for a small group of x -values, we should not expect the center to be in exactly the right place. Note: You might consider having students choose different samples from those prescribed 150

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Solutions 151 in this exercise, and then pooling the results for the whole class. With more values of x, a better picture of the sampling distribution begins to develop. Line Digits Scores x 116 14459 62 + 72 + 73 + 62 = 269 67.25 117 3816 58 + 74 + 62 + 65 = 259 64.75 118 7319 66 + 58 + 62 + 62 = 248 62 119 95857 62 + 73 + 74 + 66 = 275 68.75 120 3547 58 + 73 + 72 + 66 = 269 67.25 121 7148 66 + 62 + 72 + 74 = 274 68.5 122 1387 62 + 58 + 74 + 66 = 260 65 123 54580 73 + 72 + 74 + 82 = 301 75.25 124 7103 66 + 62 + 82 + 58 = 268 67 125 9674 62 + 65 + 66 + 72 = 265 66.25 60 62 64 66 68 70 72 74 76 78 0 1 2 3 4 Frequency x-bar value 11.8. (a) x is not systematically higher than or lower than µ ; that is, it has no particular tendency to underestimate or overestimate µ . (b) With large samples,
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This note was uploaded on 11/23/2010 for the course STAT 2325151 taught by Professor T during the Spring '10 term at Waters College.

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ch11 - Chapter 11 Solutions 11.1. Both 283 and 311 pushes...

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