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Lobster trap placement. Refer to the Bulletin of Marine Science (April 2010) study of lobster trap placement Exercise. Recall that you used a 95% confidence interval to estimate the mean trap spacing (in meters) for the population of red spiny lobster fishermen fishing in Baja California Sur, Mexico. How many teams of fishermen would need to be sampled in order to reduce the width of the confidence interval to 5 meters? Use the sample standard deviation from Exercise 5.35 in your calculation. 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 86 From Shester, G. G. "Explaining catch variation among Baja California lobster fishers through spatial analysis of trap-placement decisions." Bulletin of Marine Science , Vol 86, 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.Aluminum cans contaminated by fire. A gigantic warehouse located in Tampa, Florida, stores approximately 60 million empty aluminum beer and soda cans. Recently, a fire occurred at the warehouse. The smoke from the fire contaminated many of the cans with blackspot, rendering them unusable. A University of South Florida statistician was hired by the insurance company to estimate p, the true proportion of cans in the warehouse that were contaminated by the fire. How many aluminum cans should be randomly sampled to estimate the true proportion to within.02 with 90% confidence?Pitch memory of amusiacs. Refer to the Advances in Cognitive Psychology (Vol. 8, 2010) study of pitch memory of amusics, Exercise. Recall that diagnosed amusiacs listened to a series of tone pairs and were asked to determine if the tones were the same or different. In the first trial, the tones were separated by 1 second; in the second trial, the tones were separated by 5 seconds. The variable of interest was the difference between scores on the two trials. How many amusiacs would need to participate in the study in order to estimate the true mean score difference for all amusiacs to within .05 with 90% confidence? Pitch memory of amusiacs. Congenital amusia is a disorder that impacts one's perception of music. A team of psychologists and neuroscientists tested the pitch memory of individuals diagnosed with amusia and reported their results in Advances in Cognitive Psychology (Vol 6. 2010). Each in a sample of 17 amusiacs listened to a series of tone pairs, where each tone pair was a standard tone followed by a comparison tone. For each tone pair, the subjects were asked to determine if the tones were the same or different. In one trial, the tones were separated by 1 second. In a second trial, the tones were separated by 5 seconds. (In theory, the longer the delay between tones, the less likely one is to detect a difference between the tones. ) Scores in the two trials were compared for each amusiac. The mean score difference was .11 with a standard deviation of .19. Use this information to form a 90%% confidence interval for the true mean score difference for all amusiacs. Interpret the result. What assumption about the population of score differences must hold true for the interval to be valid?Shopping on Black Friday. Refer to the International Journal of Retail and Distribution Management (Vol. 30, 2011) survey of Black Friday shoppers, Exercise 7.22 (p. 325). One question was "How many hours do you usually spend shopping on Black Friday?" 3. How many Black Friday shoppers should be included in a sample designed to estimate (with 95% confidence) the average number of hours spent shopping on Black Friday if you want the estimate to deviate no more than .5 hour from the true mean? b. Devise a sampling plan for collecting the data that will likely result in a representative sample. (Reference Exercise 7.22) Shopping on Black Friday. The day after Thanksgiving- called Black Friday-is one of the largest shopping days in the United States. Winthrop University researchers conducted interviews with a sample of 38 women shopping on Black Friday to gauge their shopping habits and reported the results in the International Journal of Retail and Distribution Management (Vol. 30, 2011). One question was "How many hours do you usually spend shopping on Black Friday?" Data for the 38 shoppers are listed in the accompanying table. a. Describe the population of interest to the researchers. b. What is the quantitative variable of interest to the researchers? c. Use the information in the table to estimate the population mean number of hours spent shopping on Black Friday with a 95% confidence interval. d. Give a practical interpretation of the interval. e. A retail store advertises that the true mean number of hours spent shopping on Black Friday is 5.5 hours. Should the store be sued for false advertising? Explain. 4 3 16 5 6 6 5 5 4 4 4 7 12 5 6 10 5 6 10 11 Source: Thomas, 1. R, and I'cler, C "An exploratory investigation of Black Hiday consumption rituals." International Journal of Retail and Diminution Management, Val 10, No. 7 2011 (Table !).Study of aircraft bird strikes. Refer to the International Journal for Traffic and Transport Engineering (Vol. 3, 2013) study of aircraft bird strikes at a Nigerian airport, Exercise 7.68 (p. 343). Recall that an air traffic controller wants to estimate the true percentage of aircraft bird strikes that occur above 100 feet. Determine how many aircraft bird strikes need to be analyzed in order to estimate the true percentage to within 5%% if you use a 95% confidence interval. [Reference Exercise 7.69) Study of aircraft bird strikes. As worldwide air traffic volume has grown over the years, the problem of airplanes striking birds and other flying wildlife has increased dramatically. The International Journal for Traffic and Transport Engineering (Vol. 3, 2013) reported on a study of aircraft bird strikes at Aminu Kano International Airport in Nigeria. During the survey period, a sample of 44 aircraft bird strikes were analyzed. The researchers found that 38 of the 44 bird strikes at the airport occurred above 100 feet. Suppose an airport air traffic controller estimates that less than 70% of aircraft bird strikes occur above 100 feet. Comment on the accuracy of this estimate. Use a 95% confidence interval to support your inference.Bacteria in bottled water. Is the bottled water you drink safe? The Natural Resources Defense Council warns that the bottled water you are drinking may contain more bacteria and other potentially carcinogenic chemicals than are allowed by state and federal regulations. Of the more than 1,000 bottles studied, nearly one-third exceeded government levels. Suppose that the Natural Resources Defense Council wants an updated estimate of the population proportion of bottled water that violates at least one government standard. Determine the sample size (number of bottles) needed to estimate this proportion to within 1 0.01 with 99% confidence.
