E t f the p value is the probability that the

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(e) T F The p -value is the probability that the alternative hypothesis ( H a ) is true. The p -value is the probability that we observe a test statistic at least as extreme as the one we have observed, assuming the null hypothesis is true MAX=11
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Exam II Stat 226 Fall 2018 – FORM A : KEY Page 8 5. US Trade Deficit. Often, politicians and market experts will claim that the United States trade deficit has increased due to increased imports of manufactured goods from China and Mexico and a decline in the American manufacturing sector. Others may claim that a new tariff policy has actually decreased the U.S. trade deficit, so that we are exporting more than importing. Below is JMP output for a dataset of a random sample from the monthly change in the U.S. trade deficit from 1992 to the present (in $ millions). If the value is negative, the trade deficit has increased. If it is positive, the trade deficit has decreased. Suppose we want to test the claim that, on average, the US trade deficit has decreased in the last 26 years (i.e., the average change in trade deficit is greater than zero). The population parameter is μ = the mean change in U.S. trade deficit for all months from 1992 through 2018. We will conduct the test at the α = 0 . 05(0 . 1) significance level. (a) [4pts.] For the parameter of interest defined above, provide the null and alternative hypotheses (all measurements are in $millions). H 0 : μ = 0 vs. H a : μ > 0 (b) [4pts.] Using the JMP output, calculate or simply report the test statistic, degrees of freedom, and the p -value for this hypothesis test in the blanks below. Degrees of Freedom: Form A: 312 Form B: 284 Test Statistic: Form A: -0.7825 Form B: -.4303 p -value: Form A: .7827 Form B: .6663 (c) [3pts.] Fill in the blanks: Since the p - value is > than the significance level α , we fail to reject the null hypothesis. MAX=11
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Exam II Stat 226 Fall 2018 – FORM A : KEY Page 9 (d) [3pts.] Using the significance level in question (5c), fill in the blanks below to write the appro- priate conclusion for this test in the context of the data: There is NOT statistically significant evidence that the mean change in U.S. trade deficit for all months from 1992 through 2018 is greater than 0 dollars. (e) [2pts.] Fill in the blanks: A Type II Error is concluding that the mean change in U.S. trade deficit for all months from 1992 through 2018 is equal to $0 , when in reality it is greater than $0 . (f) [1pt.] Before taking a sample to conduct the hypothesis test above at α = 0 . 05 significance level, what is the probability of concluding that the trade deficit has changed in the last 26 years, if in reality, it has NOT changed? Probability: 0 . 05 (Form B: 0 . 1) (= α ) (g) [3pts.] Suppose we want to test the hypothesis that the mean change in U.S. net trade flows for all months from 1992 through 2018 is actually 120 $million (Form B: 300 $million), at a α = 0 . 05(0 . 1) signficance level ( H 0 : μ = 120(300) vs. H a : μ 6 = 120(300)). If a 95% confidence interval for μ is ( - 451 , 194) (Form B:( - 415 , 266) ), would we reject or fail to reject the null hypothesis? Clearly explain your answer.
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  • Spring '08
  • ABBEY
  • Statistical hypothesis testing

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