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Statistical Hypothesis Testing and Confidence Intervals: Analyzing Real-World Data - Document preview page 1

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Statistical Hypothesis Testing and Confidence Intervals: Analyzing Real-World Data

Application of hypothesis testing and confidence intervals in real-world datasets.

Lily Green
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Statistical Hypothesis Testing and Confidence Intervals: Analyzing Real-World Data - Page 1 preview imageStatistical Hypothesis Testing and Confidence Intervals: AnalyzingReal-World DataQuestion 1A study was conducted to estimateμ, the mean number ofweekly hours that U.S. adults use computers at home.Suppose a random sample of 81 U.S. adultsgives a meanweekly computer usage time of 8.5 hours and that from priorstudies, the population standard deviation is assumed to beσ= 3.6 hours.A similar study conducted a year earlier estimated thatμ, themean number of weekly hours that U.S. adults usecomputers at home, was 8 hours. We would like to test (atthe usual significance level of 5%) whether thecurrentstudy provides significant evidence that this mean haschanged since the previous year.Using a 95% confidence interval of (7.7, 9.3), which of thefollowing is an appropriate conclusion?AThe current studydoesprovide significant evidencethat the mean number of weekly hours has changedover the past year, since 8 falls outside the confidenceinterval.BThe current studydoes notprovide significantevidence that the mean number of weekly hours haschanged over the past year, since 8 falls outside theconfidence interval.CThe current studydoesprovide significant evidencethat the mean number of weekly hours has changedover the past year, since 8 falls inside the confidenceinterval.DThe current studydoes notprovide significantevidence that the mean number of weekly hours haschanged over the past year, since 8 falls inside the
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Statistical Hypothesis Testing and Confidence Intervals: Analyzing Real-World Data - Page 3 preview imageconfidence interval.ENone of the above. You cannot draw a conclusionbecause the only way to reach a conclusion is to find thep-value of the test.Question 2Which of the following facts about the p-value of a test iscorrect? Check all that apply.AThe p-value is calculated under the assumption that thenullhypothesis is true.BThe smaller the p-value, the more evidence the dataprovide against H0.CThe p-value can have values between-1 and 1.Question 3In June 2005, a CBS News/NY Times poll asked a randomsample of 1,111 U.S. adults the following question: "What doyou think is the most important problem facing this countrytoday?" Roughly 19% of those sampled answered "the war inIraq" (while the rest answered economy/jobs, terrorism,healthcare, etc.). Exactly a year prior to this poll, in June of2004, it was estimated that roughly 1 out of every 4 U.S.adults believed (at that time) that the war in Iraq was themost important problem facing the country.We would like to test whether the 2005 poll providessignificant evidence that the proportion of U.S. adults whobelieve that the war in Iraq is the most important problemfacing the U.S. has decreased since the prior poll.Which of the following are the appropriate hypotheses in thiscase?AH0: p = 0.19 vs. Ha: p < 0.19BH0: p = 0.19 vs. Ha: p > 0.19CH0: p< 0.25 vs. Ha: p = 0.25
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