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CI: x z*sample AP Statistics Ms. Williams QUIZ Name:______________ Chapter 10 MULTIPLE CHOICE (1 point each) 1. You have measured the systolic blood pressure of a random sample of 25 employees of a company. A 95% confidence interval for the mean systolic blood pressure for the employees is computed to be (122,138). Which of the following statements gives a valid interpretation of this interval? (a) If the sampling procedure were repeated many times, then approximately 95% of the resulting confidence intervals would contain the mean systolic blood pressure for employees in the company. (b) About 95% of the employees in the company have a systolic blood pressure between 122 and 138. (c) About 95% of the sample of employees have a systolic blood pressure between 122 and 138. (d) If the sampling procedure were repeated many times, then approximately 95% of the sample means would be between 122 and 138. (e) The probability that the sample mean falls between 122 and 138 is equal to 0.95. 2. An engineer is investigating the strength of a new type of fastener. The only information she has right now is that the strength of a similar fastener has a standard deviation of 35. Assuming that the new fasteners have the same standard deviation, how many fasteners should she test so that she can be 99% confident that the sample mean will be within 10 of the true mean strength? Choose the answer that is closest to your computed value. (a) 15 (b) 30 (c) 50 (d) 80 (e) 325 3. A study conducted by an airline showed that a random sample of nine of its passengers disembarking at the Winnipeg airport, took an average of 24.1 minutes to claim their luggage. From a previous survey it was willing to assume that time to claim luggage is normally distributed with a variance of 18 (min2). A 95% confidence interval for the mean time to claim one’s luggage has endpoints. (a) 24.1 ± 8.32 (b) 24.1 ± 3.92 (c) 24.1 ± 2.77 (d) 24.1 ± 3.26 (e) 24.1 ± 9.78 4. Consider the following graph of the mean yield of barley in 1980, 1984,and 1988 along with a 95% confidence interval. Which of the following is INCORRECT? (a) Since the confidence intervals for 1984 and 1980 have considerable overlap, there is little evidence that the sample means differ. (b) Since the confidence intervals for 1988 and 1980 do not overlap, there is good evidence that their respective population means differ. (c) The sample mean for 1984 is about 195 g/400 m2. (d) The sample mean for 1988 is less than the sample mean for 1984. (e) The estimate of the population mean in 1988 is more precise than that for 1980 because the confidence interval for 1988 is narrower than that for 1980. 5. A very simple interval estimator for μ is ( x 2 , x 2 ) Which of the following statements is/are true if the sample size, n, is “large”? (a) This interval will contain the true value of μ approximately 95 times out of one hundred. (b) This interval is an approximate 95% confidence interval for μ (c) This interval is too narrow to be a useful interval estimator for μ. (d) This interval will contain the true value of μ 997 time out of 1000. (e) Both (a) and (b) are true. AP Statistics Ms. Williams 6. A 95% confidence interval for p the proportion of Canadian beer drinkers who prefer Lion Red was found to be (0.236 to 0.282). Which of the following is correct? (a) About 95% of beer drinkers have between a 23.6% and a 28.2% chance of drinking Lion Red. (b) There is a 95% probability that the sample proportion lies between 0.236 and 0.282. (c) If a second sample was taken, there is a 95% chance that its confidence interval would contain 0.25. (d) This confidence interval indicates that we would reject the hypothesis Ho: p=0.25. (e) we are reasonably certain that the true proportion of beer drinkers who prefer Lion Red is between .24 and .28. 7. To determine the reliability of experts used in interpreting the results of polygraph examinations in criminal investigations, 280 cases were studied. The results were: If the hypotheses were HO: suspect is innocent & Ha: suspect is guilty, then how many investigations led to a type I error? (a) 131 (b) 15 (c) 9 (d) 125 (e) 24 8. In a statistical inference test with Ho : μ = 10 and Ha : μ 10 and = 0.05 (a) 95% of the time we will make an incorrect inference (b) 5% of the time we will say that there is a real difference when there is no difference (c) 5% of the time we will say that there is no real difference when there is a difference (d) 95% of the time the null hypothesis will be correct (e) 5% of the time we will make a correct inference 9. A p-value is the area under the normal curve after a z-score is calculated. This is compared to the area under the curve for the significance level. For example, a significance level of 5% would yield an area under the curve that is significant of .05. Which of the following statements is correct? (a) An extremely small p-value indicates that the actual data differs markedly from that expected if the null hypothesis were true. (b) The p-value measures the probability that the hypothesis is true. (c) The p-value measures the probability of making a Type II error. (d) The larger the p-value, the stronger the evidence against the null hypothesis (e) A large p-value indicates that the data is consistent with the alternative hypothesis. The next six questions refer to the following situation. DDT is an insecticide that accumulates up the food chain. Predator birds can be contaminated with quite high levels of the chemical by eating many lightly contaminated prey. One effect of DDT upon birds is to inhibit the production of the enzyme carbonic anhydrase which controls calcium metabolism. It is believed that this causes egg shells to be thinner and weaker than normal and makes the eggs more prone to breakage. (This is one of reasons why the condor in California is near extinction.) An experiment was conducted where 16 sparrow hawks were fed a mixture of 3 ppm dieldrin and 15 ppm DDT (a combination often found in contaminated prey). The first egg laid by each bird was measured and the mean shell thickness was found to be 0.19 mm with a standard deviation of 0.01 mm. A normal egg shell has a mean thickness of 0.2 mm. AP Statistics Ms. Williams 10. The null and alternate hypotheses are: (a) HO: μ = 0.2 Ha: μ < 0.2 (b) HO: μ < 0.2 Ha: μ = 0.2 (c) HO: μ = 0.19 Ha: μ < 0.19 (d) HO: μ = 0.19 Ha: μ = 0 (e) HO: μ = 0.2 Ha: μ 0.2 11. The value of the test statistic (the z-score for the actual data) is: (a) -1.00 (b) -4.00 (c) 0.01 (d) 1.96 (e) 1.75 12. This is a _____ sided test of significance. (a) 1 (b) 2 (c) 3 (d) can not be determined 13. The null hypothesis will be rejected (=0.05) if the test statistic is less than: (a) -2.1314 (b) -1.7530 (c) -1.9600 (d) -1.6450 (e) -1.7459 14. The outcome of the statistical inference is to: (a) reject HO (b) fail to reject HO 15. Write a sentence on the back of the scantron that details the outcome of the test in the context of the scenario. 16. Resting pulse rate is an important measure of the fitness of a person’s cardiovascular system with a lower rate indicative of greater fitness. The mean pulse rate for all adult males is approximately 72 beats per minute. A random sample of 25 male students currently enrolled in the Faculty of Agriculture and now taking 5.211 was selected and the mean pulse resting pulse rate was found to be 80 beats per minute with a standard deviation of 20 beats per minute. The experimenter wishes to test if the students are less fit, on average, than the general population. A possible Type II error would be to: (a) Conclude that the students are less fit (on average) than the general population when in fact they have equal fitness on average, . (b) Conclude that the students have the same fitness (on average) as the general population when in fact they are less fit on average. (c) Conclude that the students have the same fitness (on average) as the general population when in fact they are the same fitness level on average. (d) Conclude that the students are less fit (on average) than the general population, when, in fact, they are less fit on average. (e) Conclude that the students have the same fitness (on average) when in fact they are more fit on average. 17. In a test of H0 : p = 0.4 against Ha: p 0.4, a sample of size 100 produces Z=1.28 for the value of the test statistic. This a _____ sided test of significance. (a) 1 (b) 2 (c) 3 (d) can not be determined 18. According to the problem above, the p-value (or “observed area under the tail”) of the test is approximately equal to: (a) 0.90 (b) 0.40 (c) 0.05 (d) 0.20 (e) 0.10 AP Statistics Ms. Williams 19. It is believed that at least 60% of voters from a certain region in Canada favor the free trade agreement (FTA). A recent poll indicated that out of 400 randomly selected individuals, 250 favored the FTA. At the 5% level of significance, we would: (a) Fail to reject H0 because the calculated value of the test statistic is 1.033 which is less than 1.645. (b) Fail to reject H0 because the calculated value of the test statistic is 1.033 which is less than 1.96. (c) Fail to reject H0 because the calculated value of the test statistic is 1.0204 which is less than 1.96. (d) Fail to reject H0 because the calculated value of the test statistic is 1.0204 which is less than 1.645. (e) Not need to test because everyone knows that FTA is good. The next two questions refer to the the following situation. The University of Manitoba research station wishes to investigate if a new variety of wheat is more resistant to a disease than an old variety at the 10% significance level. It is known that this disease strikes approximately 15% of all plants of the old variety. A field experiment was conducted, and of 120 new plants, 12 became infected. 20. The null and alternative hypothesis are: (a) H0 : p = 0.10 Ha : p > 0.15 (b) H0 : p = 0.10 Ha : p > 0.10 (c) H0 : p = 0.15 Ha : p 0.15 (d) H0 : p = 0.15 Ha : p < 0.15 (e) H0 : p = 0.15 Ha : p > 0.15 21. Calculate z* and the test statistic (the z-score from the data). (a) -1.28 and -1.53 (b) −1.10 and 1.53 (c) 1.28 and-1.83 (d) −1.83 and 1.10 (e) −1.53 and -1.83 22. Write a sentence on the back of the scantron that details the outcome of the test in the context of the scenario. 23. If an inference test shows that there is a significant difference between the sample and the population it means that: (a) there is a large numerical difference in the value between the sample and the population (b) the difference between the value of the sample and the value of the population is due to sampling error only (c) the sample and the population differ but could still be relatively close in value (d) the sample was biased and a new sample would likely yield another result (e) 24. If the null hypothesis is not rejected it means that: (a) with complete certainty, there is no difference between the sample and the population (b) the researcher can make a claim that there is absolutely no difference between the data sets (c) people can feel comfortable believing that without a doubt the researcher has proven no difference between the data (d) there is still a tiiiiiiiny chance that there really is a difference (e) from this point forward, 100% of the time the data from other samples should yield the same result 25. What is a statistical inference? (a) A set of data selected from a larger set of data. (b) A statement made about a sample based on the measurements in that sample. (c) A decision, estimate, prediction, or generalization about the population based on information contained in a sample. (d) A decision, estimate, prediction or generalization about sample based on information contained in a population. (e) A set of data that characterizes some phenomenon.