REVIEW CHAPTER 10 1. A random sample of 85 students in Chicago city high schools take a course designed to improve SAT scores. Based on these students, a 90% confidence interval for the mean improvement in SAT scores for all Chicago city high school students is computed as (72.3, 91.4) points. The correct interpretation of this interval is (a) 90% of the students in the sample improved their scores by between 72.3 and 91.4 points (b) 90% of the students in the population should improve their scores by between 72.3 and 91.4 points (c) None of the above 2. Crop researchers plant 100 plots with a new variety of corn. The average yield for these plots is x = 130 bushels per acre. Assume that the yield per acre for the new variety of corn follows a normal distribution with unknown mean u and standard deviation = 10 bushels per acre. A 90% confidence interval for is (a) 130 1.645. (b) 130 1.96. (c) 130 16.45. 3. A random sample is collected of size n from a population with standard deviation and with the data collected a 95% confidence interval is computed for the mean of the population. Which of the following would produce a new confidence interval with smaller width (smaller margin of error) based on these same data? (a) Increase . (b) Use a smaller confidence level. (c) Use a smaller sample size. 4. To assess the accuracy of a kitchen scale a standard weight known to weigh 1 gram is weighed a total of n times and the mean, x , of the weighings is computed. Suppose the scale readings are normally distributed with unknown mean, m, and standard deviation = 0.01 g. How large should n be so that a 90% confidence interval for m has a margin of error of 0.0001? (a) 165 (b) 27061 (c) 38416 Feb 2005 Rev Ch 10 p. 2 5. The times for untrained rats to run a standard maze has a N (65, 15) distribution where the times are measured in seconds. The researchers hope to show that training improves the times. The alternative hypothesis is (a) H a : 65. (b) H a : x 65. (c) H a : 65. 6. A social psychologists reports that “in our sample, ethnocentrism was significantly higher (P 0.05) among church attendees than among non-attendees.” This means (a) ethnocentrism was a least 5% higher among church attendees than among non- attendees. (b) the observed differences between church attendees and non-attendees account for all but 5% of those sampled. These results are quite meaningful and should be investigated further (c) if there is actually no difference in ethnocentrism between the church attendees and non-attendees, the chance that we would observe a difference as large or larger than we did is less than 5% 7. The distribution of times that a company’s service technicians take to respond to trouble calls is normal with mean and standard deviation = 0.25 hours. The company advertises that its service technicians take an average of no more than 2 hours to respond to trouble calls from customers. From a random sample of 25 trouble calls, the average time service technicians took to respond was 2.10 hours. How strong is the evidence against the companies claim? Based on these data, the P – value of the appropriate test is (a) less than 0.0002. (b) 0.0228. (c) 0.0456. 8. Suppose we are testing the null hypothesis H 0 : = 50 and the alternative H a : 50 for a normal population with = 6. The 95% confidence interval for the mean is (51.3, 54.7). Then (a) the P – value for the test is greater than 0.05. (b) the P – value for the test is less than 0.05. (c) the P – value for the test could be greater or less than 0.05. It can’t be determined without knowing the sample size. Ch 10 p. 3 9. Suppose that the population of the scores of all high school seniors that took the SAT- V (SAT verbal) test this year follows a normal distribution with mean = 480 and standard deviation = 90. A report claims that 10,000 students who took part in a national program for improving one’s SAT-V score had significantly better scores (at the 0.05 level of significance) than the population as a whole. In order to determine if the improvement is of practical significance one should (a) find out the actual mean score of the 10,000 students. (b) find out the actual P – value (c) use a two-sided test rather than the one-sided test implied by the report. 10. Does taking garlic tablets twice a day provide significant health benefits? To investigate this issue, a researcher conducted a study of 50 adult subjects who took garlic tablets twice a day for a period of six month At the end of the study, 100 variables related to the health of the subjects were measured on each subject and the means compared to known means for these variables in the population of all adults. Four of these variables were significantly better (in the sense of statistical significance at the 5% level for the group taking the garlic tables as compared to population as a whole, and one variable was significantly better at the 1% level for the group taking the garlic tablets as compared to the population as a whole. It would be correct to conclude (a) there is good statistical evidence that taking garlic tablets twice a day provides some health benefits. (b) there is good statistical evidence that taking garlic tablets twice a day provides benefits for the variable that was significant at the 1% level. We should be somewhat cautious about making claims for the variables that were significant at the 5% level. (c) None of the above. Rev Ch 10 p. 4 11. A significance test was performed to test the null hypothesis H 0 : = 5 verses the alternative H a : 5. The test statistic is z = 1.5. The alpha level is .05. the P – value for this test is approximately ___. 12. A local chamber of commerce claims that the mean family income level in a city is $12,250. An economist runs a hypothesis tests, using a sample of 135 families, and finds a mean of $11,500 with a standard deviation of $3180. Should the $12,250 claim be rejected at a 5% level of significance? Test the hypothesis that the mean family income is $12,250. 13. Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district. 114 100 104 89 102 91 114 114 103 105 108 130 120 132 111 128 118 119 86 72 111 103 74 112 107 103 98 96 112 112 93 Treat the 31 girls as an SRS of all seventh-grade girls in the school district. Suppose that the standard deviation of IQ scores in this population is known to be = 15. a) Give a 95% confidence interval for the mean IQ score in the population. b) Is there significant evidence at the 5% level that the mean IQ score in the population differs from 100? Give appropriate statistical evidence to support your conclusion. c) In fact, the scores are those of all seventh-grade girls in one of the several schools in the district. Explain carefully why your results from (a) and (b) cannot be trusted.
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