0225 because 00225 001 we would not reject the null

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shows an empirical p-value of 0.0225. Because 0.0225 > 0.01, we would not reject the null hypothesis at the 0.01 level and conclude that this firing process was not more likely to fire individuals with larger ages. Note: You could also carry out this simulation in R > I = 10000; diff = 0 > for (i in 1:I){ rerandom = sample(age) diff[i] = mean(rerandom[1:3])-mean(rerandom[4:10]) } (d) A two-sample t -test in Minitab or R: Now p-value < 0.01, and we would reject the null hypothesis at the 0.01 level and conclude that this firing process was more likely to fire individuals with larger ages. (e) The two-sample t -test yields a much smaller p-value, about 0.006, which implies much stronger evidence of an underlying age difference between the two populations (fired and not fired). However, because of the small sample sizes (especially with the unbalanced groups), we would have major concerns about using the t -procedures for this study. The empirical p-value from the simulated randomization test is more trustworthy. In fact, in this study, it’s probably more work than we need to do, because with only 120 possible combinations it is not unreasonable to calculate the exact p-value.
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¤ Chance/Rossman, 2015 ISCAM III Example 4.2 308 Example 4.2: Speed Limit Changes Try these questions yourself before you use the solutions following to check your answers. In 1995, the National Highway System Designation Act abolished the federal mandate of 55 miles per hour maximum speed limit and allowed states to establish their own limits. Of the 50 states (plus District of Columbia), 32 increased their speed limits in 1996. The data in TrafficFatalities.txt shows the percentage change in interstate highway traffic fatalities from 1995 to 1996 and whether or not the state increased their speed limit. (Data from the National Highway Traffic Safety Administration as reported in Ramsey and Schafer, 2002.) (a) Identify the observational units and response variable of interest. Is this a randomized experiment or an observational study? (b) Produce numerical and graphical summaries of these data and describe how the two groups compare. (c) Are the technical conditions for a two-sample t -test met for this study? Explain. (d) Carry out a two-sample t -test to determine whether the average percentage change in interstate highway traffic fatalities is significantly higher in states that increased their speed limit. If you find a significant difference, estimate its magnitude with a confidence interval. (e) Discuss what the p-value in (d) measures.
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Chance/Rossman, 2015 ISCAM III Example 4.2 309 Analysis (a) The observational units are the 50 states (and the District of Columbia). The response variable of interest is the percentage change in traffic fatalities from 1995 to 1996 (quantitative). This is an observational study because the researchers did not randomly assign which states would increase their speed limits.
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