786 APPENDIX D 6. -19.9 min 6 m 6 50.4 min. The confidence interval includes 0 (on time), so the on-time performance looks reasonably good. The confidence interval is wide, so the population mean delay time is not estimated with much accuracy. 7. 27.8 min 6 s 6 85.6 min 8. Answer varies, but this result is typical: 10.1 min 6 s 6 58.8 min. 9. a. Yes, the requirements are satisfied. 8.8 seconds 6 m 6 59.3 seconds. b. Construction of a confidence interval estimate of s has a fairly strict requirement that the sample should be from a population with a normal distribution, regardless of the sample size. That requirement is not satisfied. 19 of the 36 times are 0 seconds, so the sample does not appear to be from a population having a normal distribution. 10. a. The requirements are satisfied, and here is the confidence interval: 27.03 cm 6 m 6 33.07 cm. b. The requirements are satisfied, and here is the confidence interval: 2.91 cm 6 s 6 7.72 cm. Chapter 7: Cumulative Review Exercises 1. x = 1.28 W>kg, median = 1.30 W>kg, s = 0.18 W>kg, s2 = 0.03 1W>kg22, range = 0.60 W>kg. These results are statistics. 2. Significantly low values are two standard deviations below the mean or lower, so significantly low values are 0.92 W>kg or lower; significantly high values are two standard deviations above the mean or higher, so significantly high values are 1.64 W>kg or higher. Because the lowest value of 0.9 W>kg is less than 0.92 W>kg, it is significantly low. 3. Ratio level of measurement; continuous data. 4. The graphs suggest that the sample appears to be from a population having a distribution that is approximately normal. 5. 1.16 W>kg 6 m 6 1.40 W>kg. We have 95% confidence that the limits of 1.16 W>kg and 1.40 W>kg contain the actual value of the population mean m. 6. 130 cell phones 7. a. 0.0691 (Table: 0.0694) b. 1.37 W>kg (Table: 1.36 W>kg) 8. a. 0.932 6 p 6 0.959 b. Based on the result from part (a), it is clear that the majority of the population does not feel that the song is too offensive. c. Because the respondents chose to respond, the survey involves a self-selected or voluntary response sample, so the results are very questionable. Given that the respondents are a selfselected sample, we don’t really know anything about the population. 9. 63.9% 6 p 6 68.1%. CVS Pharmacy sells flu shots and could potentially benefit from the widespread belief that there will be high demand for flu shots, so there is a potential for bias (although the Harris Poll would likely conduct the survey without any bias). 10. a. 39.909 km>h 6 m 6 40.531 km>h b. Given that the speeds are listed in order by year, another tool that would be more helpful is a time series graph of the speeds. The time series graph could reveal any pattern of change over time. The time series graph of the listed data (see next page) does not reveal any notable pattern of change over time. c. The confidence interval from the bootstrap method is not very different from the confidence interval found using the methods of Section 7-3. Because a histogram or normal quantile plot shows that the sample appears to be from a population not having a normal distribution, the bootstrap confidence interval of 2.5 6 s 6 3.3 would be a better estimate of s. 25. Answers vary, but here is a typical result using 10,000 bootstrap samples: 1.7 6 m 6 3.3. This result is very close to the confidence interval of 1.6 6 m 6 3.3 found using 1000 bootstrap samples. In this case, increasing the number of bootstrap samples from 1000 to 10,000 does not have much of an effect on the confidence interval. 27. The histogram of the 1000 bootstrap sample means is approximately symmetric as required. Chapter 7: Quick Quiz 1. 19.1% 2. We have 95% confidence that the limits of 17.5% and 20.6% contain the true value of the percentage of motorcycle owners who are women. 3. z = 2.576 (Table: 2.575) 4. 36.9% 6 p 6 43.1% 5. 2401 6. 374 (Table: 373) 7. There is a loose requirement that the sample values are from a normally distributed population. 8. The degrees of freedom is the number of sample values that can vary after restrictions have been imposed on all of the values. For the sample data described in Exercise 7, df = 5. 9. t = 2.571 10. No, the use of the x2 distribution has a fairly strict requirement that the data must be from a normal distribution. The bootstrap method could be used to find a 95% confidence interval estimate of s. Chapter 7: Review Exercises 1. a. 97 b. 93 c. No, in this case the sample size doesn’t change much at all. 2. 163 3. a. 701 b. 67.1% 6 p 6 72.8% c. 70%; {2.8 percentage points [or {2.9 percentage points if using the confidence interval limits from part (b)] d. No. Because 61% is not included in the confidence interval, it does not appear that the responses are consistent with the actual voter turnout. 4. 30.7 minutes 6 m 6 52.3 minutes. We have 95% confidence that the limits of 30.7 minutes and 52.3 minutes contain the true value of the population mean m. 5. a. Student t distribution b. None of the three distributions is appropriate, but a confidence interval could be constructed by using bootstrap methods. c. x2 (chi-square distribution) d. Normal distribution e. None of the three distributions is appropriate, but a confidence interval could be constructed by using bootstrap methods.
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