A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. << /BitsPerComponent 8 /ColorSpace /DeviceRGB /ColorTransform 0 /Filter /DCTDecode /Height 1027 /SMask 26 0 R /Subtype /Image /Type /XObject /Width 973 /Length 16487 >> What is meant by the term “90% confident” when constructing a confidence interval for a mean? 0000117945 00000 n Assume the underlying distribution is approximately normal. One way to lower the sampling error is to increase the sample size. �� � } !1AQa"q2���#B��R��$3br� 0000106434 00000 n \(N 7.9\left(\frac{2.5}{\sqrt{20}}\right)\). Confidence Interval for a Population Proportion. ���� JFIF �� C Explain what this confidence interval means in the context of the problem. Why? 0000250111 00000 n We need to use a Student’s-t distribution, because we do not know the population standard deviation. Why or why not? 0000107962 00000 n percent of all Asians who would welcome a Latino into their families. The standard deviation for this data to the nearest hundred is \(\sigma\) = $909,200. Assume the underlying population is normally distributed. List some factors that could affect the survey’s outcome that are not covered by the margin of error. Construct a 99% confidence interval for the population mean length of time using training wheels. endstream Forbes magazine published data on the best small firms in 2012. Suppose that the firm decided that it needed to be at least 96% confident of the population mean length of time to within one hour. \(X\) is the number of letters a single camper will send home. \(\bar{X}\) is the mean number of letters sent home from a sample of 20 campers. 0000069033 00000 n The sample standard deviation is 2.8 inches. Use the following information to answer the next two exercises: Five hundred and eleven (511) homes in a certain southern California community are randomly surveyed to determine if they meet minimal earthquake preparedness recommendations. ���� JFIF �� C stream We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Another question in the poll was “[How much are] you worried about the quality of education in our schools?” Sixty-three percent responded “a lot”. 0000248493 00000 n Create a confidence interval for the results of this study. Find the point estimate for the population mean. endobj %���� Construct a 95% confidence interval for the population mean time wasted. The Table shows the ages of the corporate CEOs for a random sample of these firms. Unoccupied seats on flights cause airlines to lose revenue. I know that σ from this population is 50 . << /Pages 8 0 R /Type /Catalog >> Construct a 95% confidence interval for the population proportion of adult Americans who are worried a lot about the quality of education in our schools. A sample of 16 small bags of the same brand of candies was selected. $4�%�&'()*56789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz�������������������������������������������������������������������������� ? \(N\left(0.61, \sqrt{\frac{(0.61)(0.39)}{1200}}\right)\). Assuming that the usage is normally distributed, provide an expression for calculating a 99% confidence interval for the mean usage in the March quarter of 2006. Legal. Explain in a complete sentence what the confidence interval means. %&'()*456789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz��������������������������������������������������������������������������� Notice the small difference between the two solutions–these differences are simply due to rounding error in the hand calculations. In words, define the random variable \(\bar{X}\). The most recent survey estimates with 90% confidence that the mean household income in the U.S. falls between $69,720 and $69,922. I know that σ from this population is 50 . Define the random variables \(X\) and \(\bar{X}\) in words. A pharmaceutical company makes tranquilizers. Construct a 95% confidence interval for the population proportion of adult Americans who feel that crime is the main problem. Explain what a “95% confidence interval” means for this study. There is a known standard deviation of 7.0 hours. We estimate with 96% confidence that the mean amount of money raised by all Leadership PACs during the 2011–2012 election cycle lies between $47,292.57 and $456,415.89. The difference between solutions arises from rounding differences. 16 0 obj Yes – this interval does not fall less than 0.50 so we can conclude that at least half of all American adults believe that major sports programs corrupt education – but we do so with only 75% confidence. It is believed that the standard deviation may have changed from the previous year. Even though the three point estimates are different, do any of the confidence intervals overlap? Construct a 98% confidence interval for the population mean weight of the candies. We will use a Student’s \(t\)-distribution, because we do not know the population standard deviation. The grams of fat per serving are as follows: 8; 8; 10; 7; 9; 9. Define the random variables \(X\) and \(P′\), in words. << /BitsPerComponent 8 /ColorSpace /DeviceRGB /ColorTransform 0 /Filter /DCTDecode /Height 1027 /SMask 24 0 R /Subtype /Image /Type /XObject /Width 973 /Length 16487 >> endobj A sample of Alzheimer's patients are tested to assess the amount of time in stage IV sleep. endobj Refer to Exercise. e. The confidence interval will decrease in size, because the sample size increased. 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