STATS Week 9 Assignment 2016

Week 9You should use Stata to help you with the problems. Use complete sentences in your summaries and becomplete enough that the summaries make sense on their own (e.g., don’t just write “Reject H0” asyour summary)Problem 5, all parts. For parts d and e, also let us know the value of the test statistic and correspondingdegrees of freedom. You might need to calculate the test statistic manually using formulas shown in theslides or in the text.Problem 7, all parts. Pay attention to the fact that apgar5 is ordinal in nature . . . it’s not continuous andthe problem even goes so far as to spell this out for you. So you should use this knowledge to decide foryourself whether it’s more appropriate to use Pearson’s or Spearman’s correlation. Problem 8, all parts. The data file water.dta is attached. Units for fluoride are in ppm (parts per million);caries is a count of the number of decayed, missing, or filled teeth (DMFT) per 100 children. (You have torealize that a given child can have multiple DMFT, which is why these counts can exceed the number of“trials” = children.)Last Question:In your very first problem set, you were given some Stata output concerning FEV (in liters), split outaccording to sex. At that time, the most that was asked of you was to write a solid descriptive paragraphabout the characteristics you observed in the sample data, commenting on things like the mean,median, various percentiles, scale/spread, and perhaps the general shape of the distribution of thesample data, taking note of any outliers. That was pretty good, but now your skills have hopefullygrown. Please go back and retrieve the fev.xls data file and maybe your original summary, just tobenchmark your progress. See if you can answer the following questions, written out and summarized ina few sentences. You’ve seen examples of these sorts of summary statements though out the class (inlecture slides and in homework solutions) and you’ve been writing some yourself. At the end, try tostring your summary sentences together into one paragraph, as you would for a ‘results’ section of amanuscript. If a graph (like a scatter plot, dotplot, or boxplot) would help you make your case, thenplease include it.1. What sort of association is there (if any) between age and FEV? What about between height and FEV?Please provide some numerical summary measure that quantifies the strength of the association, a teststatistic, and p-value to determine statistical signifi- cance of the association. Do these associationsappear linear?2. Does average FEV differ significantly between males and females? (Your arsenal of statistical toolsincludes both parametric and non-parametric ways to answer this question . . . choose the one you feelmost appropriate, but explain why you chose that method.) A test statistic, p-value and confidenceinterval for the difference would be greatly appreciated (if your method of analysis is capable ofproviding one).3. Does the proportion of smokers differ between men and women? Also estimate the proportion ofboys that smoke and the proportion of girls that smoke, each with separate 95% confidence intervals.Consider estimating a difference between the proportions, or perhaps an odds ratio; include a CI forwhichever effect you choose to report.4. Does average age differ between smokers and non-smokers? (Your arsenal of statistical tools includesboth parametric and non-parametric ways to answer this question . . . choose the one you feel mostappropriate, but explain why you chose that method.) Include a test statistic, p-value and confidenceinterval for the effect (if your method of analysis is capable of providing one).5. Does average FEV differ significantly between those who smoke and those who don’t? Which group ishigher, and by how much. Again, you’ve got some room to choose between parametric and nonparametricmethods, but defend your choice, whichever you choose. Are you concerned by your answer to the last part? In particular, does the data suggest that smoking is associated with greater FEV (lungcapacity)? Do any of your answers to some earlier parts suggest an alternate explanation for what youobserved concerning the smoking / FEV association?