AP Statistics - Chapter 6,7 Quiz Answer Section

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1 AP Statistics - Chapter 6,7 Quiz Answer Section SHORT ANSWER 1. ANS: The probability that two or more mice are caught during a single night; REF: Quiz 6.1A TOP: Discrete and Continuous Random Variables 2. ANS:. REF: Quiz 6.1A TOP: Discrete and Continuous Random Variables 3. ANS: J P(J) REF: Quiz 6.1A TOP: Discrete and Continuous Random Variables 4. ANS: µj = the mean amount of money Joe can expect to make per customer in the long run = REF: Quiz 6.1A TOP: Discrete and Continuous Random Variables 5. ANS: σ J = the average distance from the mean ($30.20) for each individual customer = REF: Quiz 6.1A TOP: Discrete and Continuous Random Variables 6. ANS: REF: Quiz 6.2A TOP: Transforming and Combining Random Variables 7. ANS: Let D = difference in scores between Mr. Cull and Mr. Voss. Then and REF: Quiz 6.2A TOP: Transforming and Combining Random Variables 8. ANS: is a statistic; is a parameter. REF: Quiz 7.1A TOP: What Is a Sampling Distribution 1

2 9. ANS: The population is all the guppies in the pet store. We ve been given the population mean and the population standard deviation cm. (b) The sample mean is cm and the sample size is (c) No, it s merely an approximation of a sampling distribution generated by simulating 200 sample means. The actual sampling distribution includes the means from all possible samples of size 10 from the population many more than 200 values. (d) 21 out of 200, or 10.5% of the sample means in our simulation are as far or farther below 5.0 as our sample was. Our sample is not sufficiently unusual to arouse suspicions about the store s claim. REF: Quiz 7.1A TOP: What Is a Sampling Distribution 10. ANS: The parameter is the proportion of people in the entire community who would answer Yes to the question. It s equal to The statistic is the proportion of people in the sample of 100 who would answer Yes to the question. (b) The sampling distribution describes the distribution of the proportion of people who would answer Yes to this question in all possible samples of size 100 from this population. (c) The mean of the statistic s sampling distribution is equal to the parameter. (d) No. As long as the sample is less than 10% of the population, the size of the population from which the sample is taken does not influence the sampling distribution. (e) Yes. The standard deviation of the sampling distribution would be larger if the sample size were smaller. REF: Quiz 7.1C TOP: What Is a Sampling Distribution 11. ANS: C has the largest bias: the center of the histogram is clearly to the left of the parameter value. (b) A has the lowest variability, since most values of the statistic are close to the parameter value. (c) Distribution A is unbiased and has the lowest variability, so it should give the best estimate. REF: Quiz 7.1C TOP: What Is a Sampling Distribution 12. ANS: (b) Since and, the distribution is approximately normal. (c) would not change, would be larger (0.073) and the distribution would be non-normal, since, which is less than 10. (d) The largest sample we can take is 50, otherwise the sample would be more than 10% of the population, and sampling without replacement would require a finite population correction to calculate standard deviation. REF: Quiz 7.2A TOP: Sample Proportions cm 2

3 13. ANS: minutes (the same as the population mean). (b) Yes. It seems reasonable to assume that the sample of 10 is less than 10% of the entire population calls.. (c) No. The population distribution is skewed, and n = 10, which is not large enough for the central limit theorem to apply. REF: Quiz 7.3A TOP: Sample Means 14. ANS: (b). (c) The mean weight of a random sample of three apples is less variable than the weight of a single randomly-selected apple, so we are less likely to get a mean weight that is 20 gm above the mean when we take a sample of three apples. REF: Quiz 7.3A TOP: Sample Means 15. ANS: No. We don t know the shape of the distribution, so we can t calculate this probability. (b). (c) Since n = 50, which is greater than 30, we can use the Normal probability distribution. (d) If the true mean amount of soda in the cans is 12 ounces, there is about a 4% chance of getting a sample mean as low or lower than 11.9 ounces. This result is unlikely enough to make us suspicious and lead us to conclude that the company is under-filling its cans of soda! MULTIPLE CHOICE 1. ANS: A /A/Correct! REF: Test 6A 3

4 2. ANS: E /E/Correct! ; REF: Test 6A 3. ANS: C /C/Correct! Binomial probability with n = 24 and p = REF: Test 6C 4. ANS: D /D/Correct! This is the definition of a sampling distribution. 5. ANS: D /D/Correct! Any time the center of a statistic s sampling distribution is at the parameter value, the statistic is unbiased. 6. ANS: C /C/Correct! The mean of the sampling distribution is the same as the mean of the population, and the standard deviation is 7. ANS: C /C/Correct! Even if the sampling distribution is non-normal, if the 10% condition is satisfied, this is the appropriate formula for the standard deviation. 8. ANS: E /E/Correct! Since n is small and we don t know the shape of the population distribution, the shape of the sampling distribution is unknown. 9. ANS: A /A/Correct! 4

5 10. ANS: B /B/Correct! This proportion is the result of a sample, so it s a statistic. 11. ANS: B /B/Correct! When the center of a statistic s sampling distribution is at the parameter value, the statistic is unbiased. 12. ANS: B /B/Correct! Since n is small and we don t know the shape of the population distribution, the shape of the sampling distribution is unknown. 13. ANS: A /A/Correct! A restatement of the central limit theorem. 14. ANS: C /C/Correct! The only condition that is required for using the formula is that samples from a finite population are less than 10% of the population size. 5