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9 At a large factory 38 workers were tested as to how fast they could do a particular job. The mean and standard deviation of the times they took to do their job were 68 seconds, and 12 seconds. Calculate a 95% confidence interval for the average time to do the job for all workers in the plant. 10 It has been hypothesized that individuals suffering from Alzheimer's disease may spend less time per night in the deeper stages of sleep. The number of minutes spent in deep sleep over a 24-hour period was recorded for sixty-one patients. The sample produced a mean of 48 minutes with a standard deviation of 14 minutes. a Compute a 95 percent confidence interval for the population mean based on this data. b What size sample do the researchers require in order to be at least 95% confidence that the sample mean is within 5 minutes of the population mean? 11 A standardized test was used to assess students' knowledge of world events. A sample of 30 students was given the test and found to have a sample mean of 58, with a standard deviation of 10. a Compute a 99% confidence interval for the population mean. Compute a 95% confidence interval for the population mean. Q 5 Compute a 90% confidence interval for the population mean. 12 A sample of students from a mathematics class were surveyed regarding the number of hours they spent studying for the last exam. A total of 47 students responded to the survey, and their mean study time was 14.6 hours with a standard deviation of 5.7 hours. a Compute a 95 percent confidence interval for the population mean based on this data. b What size sample is required in order to be at least 95% confident that the sample mean is within 60 minutes of the population mean