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CI_Means – The Monarch Butterfly Wing Area Example Use the information in the following setting to answer questions 1 through 9 As part of a larger study designed to characterize the body features of monarch butterflies that are found in California researchers captured many specimens from Oceano Dunes State Park. One of the variables of interest was the wing area. The data in Table 1 below are the results from 14 male specimens. Output 1 reports the descriptive statistics for the wing area data. The investigators would like to estimate the averge wing area of all male monarchs in California during the season that the study was completed. [Source: Samuels,M.L.,Witmer,J.A.,Schaffner,A.A, Statistics for the Life Sciences, 2012, pp 170-1, Pearson Ed, Boston] Table 1: Monarch Butterfly Wing Areas (cm2) 33.9 32.0 33.0 28.0 30.6 32.0 36.6 32.2 36.5 32.2 34.0 32.3 36.1 30.0 Output 1: Descriptive statistics for the monarch butterfly wing area data Variable wing N 14 Mean 32.814 SE Mean 0.662 StDev 2.476 Minimum 28.000 Q1 31.650 Median 32.250 Q3 34.525 Maximum 36.600 1) This study can be classified as a(n): A) Observational Study B) Controlled Experiment 2) Assume that this is a representative sample from the population of all male monarch butterflies in California during the season; the point estimate for the true average wing area for this population on this instrument is: 3) Again assume that this is a representative sample from the population of all male monarch butterflies in California during the season; the point estimate for the true standard deviation is: 4) The investigators wish to construct a 90% confidence interval (CI) for the true average wing area in the target population. Based on this, the table value used to compute the bound (margin of error) on the estimate is: Gumina/Hunter CI_Means-Monarch Wing Area.docx Page 1 of 3 CI_Means – The Monarch Butterfly Wing Area Example 5) The 90% bound (B) on the estimated wing area is: 6) Construct the 90% CI for the true average wing area for the target population 7) The English interpretation of the interval computed in Problem 6 is: 8) Based on the result from Problem 7 construct the corresponding CI diagram: 9) A recent report claimed that the average wing area for male monarch butterflies in California during the season is 35 cm2. Based on the results from Problems 7 and 8 would you agree or disagree with this claim? Agree Disagree 10) Defend your choice for Problem 9. If you answered ‘agree’ then state the direction of the difference and discuss the rationale for your conclusion. Gumina/Hunter CI_Means-Monarch Wing Area.docx Page 2 of 3 CI_Means – The Monarch Butterfly Wing Area Example Output 2: CI and hypothesis test results for the wing area study One-Sample T: wing Test of mu = 35 vs not = 35 Variable wing N 14 Gumina/Hunter Mean 32.814 StDev 2.476 SE Mean 0.662 95% CI (31.385, 34.244) T -3.30 P 0.006 CI_Means-Monarch Wing Area.docx Page 3 of 3