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Characteristics of ice-melt ponds. Refer to the University of Colorado study of ice-melt ponds in the Canadian Arctic, presented in Exercise. Environmental engineers are using data collected by the National Snow and Ice Data Center to learn how climate affects the sea ice. Data on 504 ice melt ponds are saved in the PONDICE file. Of these 504 melt ponds, 88 were classified as having "first-year ice." Recall that the researchers estimated that about 17% of melt ponds in the Canadian Arctic have firstyear ice. Use the methodology of this chapter to estimate, with 90% confidence, the percentage of all ice-melt ponds in the Canadian Arctic that have first-year ice. Give a practical interpretation of the results. Characteristics of ice melt ponds. The National Snow and Ice Data Center (NSIDC) collects data on the albedo, depth, and physical characteristics of ice melt ponds in The FREQ Procedure ICETYPE Frequency | Percent | Cumulative Frequency Cumulative Percent First-year 88 17.48 8:8 17.48 Landfast 198 38.89 284 58.35 Multi-year 220 43.75 504 100.00 ICE TYPE Landhun! Hull -your 20 90 PERCENT the Canadian Arctic. Environmental engineers at the University of Colorado are using these data to study how climate affects the sea ice. Data on 504 ice melt ponds located in the Barrow Strait in the Canadian Arctic are saved in the PONDICE file. One variable of interest is the type of ice observed for each pond, classified as firstyear ice, multiyear ice. or landfast ice. An SAS summary table and a horizontal bar graph that describe the types of ice of the 504 melt ponds are shown at the bottom of page a. Of the 504 melt ponds, what proportion had landfast ice? b. The University of Colorado researchers estimated that about 17%% of melt ponds in the Canadian Arctic have first-year ice. Do you agree? c. Convert the horizontal bar graph into a Pareto diagram. Interpret the graph.Splinting in mountain-climbing accidents. The most common injury that occurs among mountain climbers is trauma to the lower extremity (leg). Consequently, rescuers must be proficient in immobilizing and splinting of fractures. In High Altitude Medicine & Biology (Vol. 10. 2009). researchers provided official recommendations for mountain emergency medicine. As part of the document, the researchers examined the likelihood of needing certain types of splints. A Scottish Mountain Rescue study reported that there was 1 femoral shaft splint needed among 333 live casualties. The researchers will use this study to estimate the proportion of all mountain casualties that require a femoral shaft splint. a. Is the sample large enough to apply the large-sample estimation method of this section? Show why or why not. b. Use Wilson's adjustment to find a 95% confidence interval for the true proportion of all mountain casualties that require a femoral shaft splint. Interpret the result.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.Teenagers' use of emoticons in school writing. Due to the popularity of instant messaging and social networking sites among American teenagers, informal elementssuch as emoticons (e.g., the symbol ":)" to represent a smile) and abbreviations (e.g., "LOL" for "laughing out loud" have worked their way into teenagers' school writing assignments. In a survey cosponsored by the National Commission on Writing at the College Board, the Pew Infemet and American Life Project (April 2008) interviewed 700 randomly selected U.S. teenagers by telephone on their writing habits. Overall, 448 of the teenagers admitted using at least one informal element in school writing assignments. Based on the survey results, construct a 99% confidence interval for the proportion of all U.S. teenagers who have used at least one informal element in school writing assignments. Give a practical interpretation of the interval, one that is relevant to the National Commission on Writing at the College Board.Splinting in mountain-climbing accidents. The most common injury that occurs among mountain climbers is trauma to the lower extremity (leg). Consequently, rescuers must be proficient in immobilizing and splinting of fractures. In High Altitude Medicine & Biology (Vol. 10. 2009). researchers provided official recommendations for mountain emergency medicine. As part of the document, the researchers examined the likelihood of needing certain types of splints. A Scottish Mountain Rescue study reported that there was 1 femoral shaft splint needed among 333 live casualties. The researchers will use this study to estimate the proportion of all mountain casualties that require a femoral shaft splint. 3. Is the sample large enough to apply the large-sample estimation method of this section? Show why or why not. b. Use Wilson's adjustment to find a 95% confidence interval for the true proportion of all mountain casualties that require a femoral shaft splint. Interpret the result.Eye shadow, mascara, and nickel allergies. Pigmented makeup products like mascara and eye shadow may contain metal (e.g., nickel) allergens. Is a nickel allergy more likely to occur in women who report cosmetic dermatitis from using eye shadow or mascara? This was the question of interest in a paper published in the Journal of the European Academy of Dermatology and Venereology (June 2010). In a sample of 131 women with cosmetic dermatitis from using eye shadow, 12 were diagnosed with a nickel allergy. In a sample of 250 women with cosmetic dermatitis from using mascara, 25 were diagnosed with a nickel allergy. Suppose you are informed that the true proportion with a nickel allergy for one of the two groups (eye shadow or mascara) is .12. Can you determine which group is referenced? Explain.If you wish to estimate a population mean to within .2 with a 95% confidence interval and you know from previous sampling that 02 is approximately equal to 5.4, how many observations would you have to include in your sample?If nothing is known about p. .5 can be substituted for p in the sample-size formula for a population proportion. But when this is done, the resulting sample size may be larger than needed. Under what circumstances will using p = .5 in the sample-size formula yield a sample size larger than is needed to construct a confidence interval for p with a specified bound and a specified confidence level?Suppose you wish to estimate a population mean correct to within. 15 with a confidence level of 90. You do not know 02, but you know that the observations will range in value between 31 and 39. a. Find the approximate sample size that will produce the desired accuracy of the estimate. You wish to be conservative to ensure that the sample size will be ample for achieving the desired accuracy of the estimate. [Hint: Using your knowledge of data variation from Section 2.5, assume that the range of the observations will equal 40.] b. Calculate the approximate sample size, making the less conservative assumption that the range of the observations is equal to 60.In each case, find the approximate sample size required to construct a 95% confidence interval for p that has sampling error SE = .08. a. Assume that p is near .3. b. Assume that you have no prior knowledge about p. but you wish to be certain that your sample is large enough to achieve the specified accuracy for the estimate.The following is a 90%% confidence interval for p: (.28, .54). How large was the sample used to construct this interval
