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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.

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    Statistical Hypothesis Testing and Confidence Intervals: Analyzing Real - World Data Question 1 A study was conducted to estimate μ , the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be σ = 3.6 hours. A similar study conducted a year earlier estimated that μ , the mean number of weekly hours that U.S. adults use computers at home, was 8 hours. We would like to test (at the usual significance level of 5%) whether the current study provides significant evidence that this mean has changed since the previous year. Using a 95% confidence interval of (7.7, 9.3), which of the following is an appropriate conclusion? A The current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval. B The current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval. C The current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval. D The current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the

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    confidence interval. E None of the above. You cannot draw a conclusion because the only way to reach a conclusion is to find the p - value of the test. Question 2 Which of the following facts about the p - value of a test is correct? Check all that apply. A The p - value is calculated under the assumption that the null hypothesis is true. B The smaller the p - value, the more evidence the data provide against H 0 . C The p - value can have values between - 1 and 1. Question 3 In June 2005, a CBS News/NY Times poll asked a random sample of 1,111 U.S. adults the following question: "What do you think is the most important problem facing this country today?" Roughly 19% of those sampled answered "the war in Iraq" (while the rest answered economy/jobs, terrorism, healthcare, etc.). Exactly a year prior to this poll, in June of 2004, it was estimated that roughly 1 out of every 4 U.S. adults believed (at that time) that the war in Iraq was the most important problem facing the country. We would like to test whether the 2005 poll provides significant evidence that the proportion of U.S. adults who believe that the war in Iraq is the most important problem facing the U.S. has decreased since the prior poll. Which of the following are the appropriate hypotheses in this case? A H 0 : p = 0.19 vs. H a : p < 0.19 B H 0 : p = 0.19 vs. H a : p > 0.19 C H 0 : p < 0.25 vs. H a : p = 0.25

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