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STT 200 Final Exam_Practice Exam_SOLUTIONS

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STT 200 – FINAL EXAM PRACTICE EXAM – FALL 2019 Your exam will consist of a handwritten portion and a scantron portion. For the handwritten portion, you will be expected to show your work in the ... spaces provided and to write your final answer in the space indicated. Answers with insufficient supporting work will not earn any points. For the scantron portion, you will need to circle your answers on the test sheet AND bubble in your answer on a scantron sheet that will be provided for you during the exam. Only the scantron will be graded. Answers on the test sheet will be considered in case of errors. It is your responsibility to hand in the Scantron sheet, Exam and Formula sheet to the proctors and sign the Sign out sheet. HANDWRITTEN PORTION 1. Air Quality ~ Daily air quality is measured by the Environmental Protection Agency. This index reports the pollution level for five major air pollutants regulated by the Clean Air Act and calculates an overall air quality score for each day. A researcher wonders whether air quality is worse in the winter months or in the summer months. From the data recorded for the Detroit-Warren-Dearborn region in Michigan, they selected a random sample of 50 days between October and March and a sample of 55 days from April to September and calculated the summary statistics shown in the table. Months Mean air quality score SD of air quality score Winter: October to March 57.42 19.5 Summer: April to September 60.49 23.6 a. The researcher wants to use statistical inference to determine if the air quality scores are different for winter and summer months. Express the research question in terms of two competing hypotheses using appropriate notation. ??: ?? = ?? ?? ??: ?? ≠ ??, where ?? represents the population mean air quality score for winter and ?? represents the population mean air quality score for summer. b. Calculate the test statistic and the p-value for this hypothesis test. Show all work and/or calculator input/output. Graphic Calculator Input Formula and Substitution with tcdf input on Graphic Calculator 2-SampTtest ? ̅? = ??. ?? ??? = ??. ? ?? = ?? ? ̅? = ??. ?? ??? = ??. ? ?? = ?? ?? ≠ ?? Pooled: NO ? = ??. ?? − ??. ?? √???? . ?? + ???? . ?? = −?. ???? p-value = 2 x tcdf(− ????, −?. ????, 49) = 0.4694 Observed test statistic: -0.7291 and p-value: 0.4676 OR 0.4694 c. The calculated effect size for this hypothesis test has a magnitude of 0.14. Another researcher decides to replicate this study, using data from a different metropolitan region. Conducting the same test with a sample size of 40 days from winter months and 50 days from summer months, the researcher calculates a p-value of 0.053 and an effect size of magnitude 0.18. Does the second researcher’s study confirm or conflict with the findings of the first researcher. [Show More]

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