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Oil content of fried sweet potato chips. The characteristics of sweet potato chips fried at different temperatures were investigated in the Journal of Food Engineering (Sept. 2013). A sample of 6 sweet potato slices were fried at 130' using a vacuum fryer. One characteristic of interest to the researchers was internal oil content (measured in gigagrams). The results were: x- .178p/g and s - .011g/2. Use this information to construct a 95% confidence interval for the true standard deviation of the internal oil content distribution for the sweet potato chips. Interpret the result practically.Radon exposure in Egyptian tombs. Refer to the Radiation Protection Dosimetry (Dec. 2010) study of radon exposure in tombs carved from limestone in the Egyptian Valley of Kings. Exercise 7.30 (p. 334). The radon levels in the inner chambers of a sample of 12 tombs were determined, yielding the following summary statistics: $ = 3413Bq/m and s - 4,487 Bq/m]. Use this information to estimate, with 95% confidence, the true standard deviation of radon levels in tombs in the Valley of Kings. Interpret the resulting interval. Be sure to give the units of measurement in your interpretation. (Reference Exercise 7.39) Radon exposure in Egyptian tombs. Many ancient Egyptian tombs were cut from limestone rock that contained uranium. Since most tombs are not well- ventilated, guards, tour guides, and visitors may be exposed to deadly radon gas. In Radiation Protection Dosimetry (Dec. 2010), a study of radon exposure in tombs in the Valley of Kings, Luxor, Egypt (recently opened for public tours). was conducted. The radon levels-measured in becquerels per cubic meter (Bq/m )-in the inner chambers of a sample of 12 tombs were determined. For this data, assume that J = 3,643 By/m' and & = 1,187 Bq/m'.Use this information to estimate, with 95% confidence, the true mean level of radon exposure in tombs in the Valley of Kings. Interpret the resulting interval.Cheek teeth of extinct primates. Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) studyof the characteristics of cheek teeth (e.g., molars) in anextinct primate species, Exercise. Recall thatthe researchers recorded the dentary depth of molars (inmillimeters) for a sample of 18 cheek teeth extracted fromskulls. The data are repeated in the table and saved in the CHEEKTEETH file. Estimate the true standard deviationin molar depths for the population of cheek teeth in extinct primates using a 95% confidence interval. Give a practicalinterpretation of the result. Are the conditions required fora valid confidence interval reasonably satisfied? 18.12 18.55 19.48 15.70 19.36 17.83 15.94 13.25 15.83 18.12 19.70 18.13 15.78 14.02 17.00 14.02 13.98 18.20 Based on Boyer, D. M., Evans, A. R., and Jervall, J. "Evidence of dietary differentiation among Late Paleocene-Early Eocene Plesiadapids (Mammalia, Primates)." American Journal of Physical Anthropology , Vol. 142, 2010 (Table A3)Shell lengths of sea turtles. Refer to the Aquatic Biology (Vol. 0, 2010) study of green sea turtles inhabiting theGrand Cayman South Sound lagoon. Exercise 5.20 (p. 252). Recall that the data on shell length, measured in centimeters, for 76 captured turtles are saved in the TURTLES file. Use the sample data to estimate the true variance inshell lengths of all green sea turtles in the lagoon with 90% confidence. Interpret the result. Shell lengths of sea turtles. Refer to the Aquatic Biology (Vol. 9, 2010) study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, Exercise. The data on curved carapace (shell) length, measured in centimeters, for 76 captured turtles are displayed in the table and saved in the TURTLES file. Environmentalists want to estimate the true mean shell length of all green sea turtles in the lagoon. 33.96 30.37 32.57 31.50 36.46 35.54 36.16 35.32 35.09 39.55 44.33 42.73 42.15 42.43 49.96 46.04 48.76 47.78 45.81 49.05 49.65 49.71 54.29 52.01 51.15 54.42 2 52.62 53.27 54.07 50.40 53.60 51.30 54.29 54.58 55.11 57.65 56.35 55.68 58.40 58.06 57.79 65.98 57.03 57.64 59.27 64.79 61.96 60.08 62.34 63.84 60.24 64.91 60.35 62.63 63.33 63.00 64.55 60.03 64.75 60.61 69.01 65.07 65.77 65.30 68.24 65.28 67.54 68.49 56.54 65.67 70.26 70.94 70.52 72.01 74.34 81.63 3. Define the parameter of interest to the environmentalists. b. Use the data in the TURTLES file to find a point estimate of the target parameter. c. Compute a 95% confidence interval for the target parameter. Interpret the result. d. Suppose a biologist claims that the mean shell length of all green sea turtles in the lagoon is 60 cm. Make an inference about the validity of this claim. Shell lengths of sea turtles. Aquatic Biology (Vol. 9, 2010) reported on a study of green sea turtles inhabiting the Grand Cayman South Sound lagoon. The data on curved carapace (shell) length (in centimeters) for 76 captured turtles are saved in the TURTLES file. Descriptive statistics for the data are shown on the accompanying MINITAB printout. Descriptive Statistics: Length Variable No Mean StDev | Variance | Minimum | Maximum | Range Length 78 55.47 11.34 128.57 30.37 81.83 51.26 a. Locate the range of the shell lengths on the printout. b. Locate the variance of the shell lengths on the printout. c. Locate the standard deviation of the shell lengths on the printout. d. If the target of your interest is these specific 76 captured turtles, what symbols would you use to represent the variance and standard deviation?Lobster trap placement. Refer to the Bulletin of Marine Science (April 2010) observational study of teams fishing for the red spiny lobster in Baja California Sur, Mexico, Exercise. Trap spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen are repeated in the table (p. 283) and saved in the TRAPSPACE file. The researchers want to know how variable the trap spacing measurements are for the population of red spiny lobster fishermen fishing in Baja California Sur, Mexico. Provide the researchers with an estimate of the target parameter using a 90% confidence interval. 93 99 105 94 82 70 86 Based on Shester, G. G. "Explaining catch variation among Baja California lobster fishers through spatial analysis of trap-placement decisions." Bulletin of Marine Science, Vol. 80, No. 2, April 2010 (Table). Lobster trap placement. Strategic placement of lobster traps is one of the keys for a successful lobster fisherman. An observational study of teams fishing for the red spiny lobster in Baja California Sur, Mexico, was conducted and the results published in Bulletin of Marine Science (April, 2010). One of the variables of interest was the average distance separating traps-called trap spacing -deployed by the same team of fishermen. Trap spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen are shown in the accompanying table (and saved in the TRAPSPACE file). Of interest is the mean trap spacing for the population of red spiny lobster fishermen fishing in Baja California Sur, Mexico. 93 99 105 94 82 70 88 From Shester, G. G. "Explaining catch variation among Baja California lobster fishers through spatial analysis of trap-placement decisions." Bulletin of Marine Science , Vol. 80, No. 2. April 2010 (Table). pp. 479-498. Reprinted with permission from the University of Miami - Bulletin of Marine Science. a. Identify the target parameter for this study. b. Compute a point estimate of the target parameter. c. What is the problem with using the normal (z) statistic to find a confidence interval for the target parameter? d. Find a 95% confidence interval for the target parameter. e. Give a practical interpretation of the interval, part d. f. What conditions must be satisfied for the interval, part d, to be valid?Interpret the phrase "95% confident" in the following statement:"We are 95% confident that the proportion of all PCs with a computer virus falls between .12 and .18."Let *0 represent a particular value of f from Table IV of Appendix A. Find the table values such that the following statements are true" a. P(ts (0) = .05, where of = 17 b. P(f 2 10) = .005. where of = 14 c. Pits -(0 or f2 10) = .10, where di = 8 d. P(ts-10 or tz f0) = _01, where of = 22In a random sample of 400 measurements, 227 possess the characteristic of interest, A. a. Use a 05% confidence interval to estimate the true proportion p of measurements in the population with characteristic A. b. How large a sample would be needed to estimate p to within .02 with 95% confidence?Scanning errors at Wal-Mart. Refer to the National Institute for Standards and Technology (NIST) study of the accuracy of checkout scanners at Wal-Mart stores in California, presented in Exercise. NIST sets standards so that no more than 2 of every 100 items scanned through an electronic checkout scanner can have an inaccurate price. Recall that in a sample of 80 Wal-Mart stores, 52 violated the NIST scanner accuracy standard (Tampa Tribune. Nov. 22, 2005). Suppose you want to estimate the true proportion of Wal-Mart stores in California that violate the NIST standard. a. Explain why the large-sample methodology of Section 7.4 is inappropriate for this study. b. Determine the number of Wal-Mart stores that must be sampled in order to estimate the true proportion to within .05 with 90% confidence, using the large-sample method. A random sample of size n = 144 yielded p = .78. a. Is the sample size large enough to use the methods of this section to construct a confidence interval for p? Explain. b. Construct a 90% confidence interval for p. C. What assumption is necessary to ensure the validity of this confidence interval?Assessing the bending strength of a wooden roof. The white wood material used for the roof of an ancient Japanese temple is imported from Northern Europe. The wooden roof must withstand as much as 100 centimeters of snow in the winter. Architects at Tohoku University (in Japan) conducted a study to estimate the mean bending strength of the white wood roof (Journal of the International Association for Shell and Spatial Structures, Aug. 2004). A sample of 25 pieces of the imported wood was tested and yielded the following statistics on breaking strength (in MP3): X - 754.s - 10.9. 3. Estimate the true mean breaking strength of the white wood with a 90% confidence interval. Interpret the result. b. Suppose you want to estimate the true mean breaking strength of the white wood to within 4 MPa, using a 90% confidence interval. How many pieces of the imported wood need to be tested?Water pollution testing. The EPA wants to test a randomly selected sample of n water specimens and estimate p, the mean daily rate of pollution produced by a mining operation. If the EPA wants a 95%% confidence interval estimate with a sampling error of 1 milligram per liter (mg/L). how many water specimens are required in the sample? Assume that prior knowledge indicates that pollution readings in water samples taken during a day are approximately normally distributed with a standard deviation equal to 5 (mg/L)
