# I need 3 exams taken and 3 assignments done for the rest of the semester.

Complete each assignment and exam showing work and working in jmp or R, give them to me in advance so I can turn them in and I will pay $100 for each completed assignment/exam.

My first assignment is due tomorrow at 5pm and my first exam opens Monday and closes Tuesday at 10pm. I have attached the homework for you and the exam is very similar.

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Stat 587 XW Homework 4 Due Date: Saturday, June 13-th, 11:59pm ALL HOMEWORK MUST BE SUBMITTED USING CANVAS. PLEASE ATTACH ONE PDF FILE CONTAINING ANSWERS TO YOUR CHOICE OF 3 PROBLEMS. IF YOU SUBMIT MORE THAN 3 PROBLEMS, ONLY THE FIRST 3 PROBLEMS OF YOUR ASSIGNMENT WILL BE GRADED. 1. Amphetamine is a drug that suppresses appetite. In a study of this effect, a pharmacologist randomly allocated 24 rats to three treatment groups to receive an injection of amphetamine at one of two dosage levels (2.5 mg/kg and 5 mg/kg), or an injection of saline solution. She measured the amount of food consumed by each animal in the 3-hour period following the injection. The results (gm of food consumed per kg body weight) are available in amphetamine.dat. (a) Is there evidence that the amount of food consumed by animals is different among the three groups? Provide a test statistic, approximate p-value, and a conclusion, in context. (b) Test the claim that food consumption is smaller in the group receiving 5.0 mg/kg amphetamine than the group receiving the saline solution. (c) Sketch a plot of the estimated mean food consumption for each group versus amphetamine dosage levels. Describe in a few words the relationship (if any) you observe in this plot. (d) Use a linear trend contrast to test the null hypothesis of no linear trend in food consumption. Report the test statistic and p-value and a conclusion within the context of the data. 2. A plant physiologist investigated the effect of flooding on root metabolism in two tree species: flood-tolerant river birch and the intolerant European birch. Four seedlings of each species were flooded for one day and four were used as controls. The concentration of adenosine triphosphate (ATP) in the roots of each plant was measured. The data (nmol ATP per mg tissue) are shown in the table below, and are available in ATP.dat. River Birch European Birch Flooded Control Flooded Control 1.45 1.70 0.21 1.34 1.19 2.04 0.58 0.99 1.05 1.49 0.11 1.17 1.07 1.91 0.27 1.30 (a) Test the null hypothesis that the ATP concentration for the four groups is the same. Provide a test statistic, p-value, and a conclusion. (b) Determine a 95% confidence interval for the mean ATP concentration of the Flooded River Birch group. (c) Define linear combinations (that is, specify the coefficients) to measure each of the following: i. The effect of flooding in European birch ii. The difference between river birch and European birch with respect to the effect of flooding (d) Use a t-test to investigate whether flooding has the same effect in river birch and in European birch. (e) Provide a 95% confidence interval for the contrast that compares the average of the Flooded and Control River birch mean ATP levels to the average of the Flooded and Control European birch mean ATP levels. 1 3. One measure of lung function is forced vital capacity (FVC), which is the maximal amount of air a person can expire in one breath. In a public health survey, researchers measured FVC in a large sample of people. The results for male ex-smokers, stratified by age, are shown in the following table: FVC (liters) Age(years) n Mean SD 25–34 83 5.29 0.76 35–44 102 5.05 0.77 45–54 126 4.51 0.74 55–64 97 4.24 0.80 65–74 73 3.58 0.82 25–74 481 4.56 (a) Suppose it is desired to calculate a summary value for FVC in male ex-smokers. One possibility would be simply to calculate the overall mean of the 481 observed values which is 4.56 liters. Name any serious drawbacks associated with this approach. (b) Construct a 95% confidence interval for the overall mean. (c) Another summary measure is the “age-adjusted” mean, which is an estimate of the mean FVC value in a reference population with a specified age distribution. This is given by the following linear combination: L = .27Ȳ1 + .28Ȳ2 + .21Ȳ3 + .13Ȳ4 + .11Ȳ5 . Construct a 95% confidence interval for the age-adjusted mean. (d) Is this a contrast? Why or why not? (e) Based on the two confidence intervals obtained above, what can you conclude about the two measures of FVC (i.e. overall mean and age-adjusted mean)? 4. Lettuce yield The data in lettuce.csv come from a randomized experiment on the response of lettuce to additions of nitrogen fertilizer. The experiment was conducted on irrigated plots in Arizona. Plots were randomly assigned to one of four fertilizer levels: 0, 50, 100 or 150 lb. N /acre. The response is the number of lettuce heads harvested from each plot. There were four replicates of each treatment. Don’t worry about assumptions and analyze the yield data without using any transformation. (a) Test the null hypothesis of no difference among treatments. Report the test statistic and p-value. (b) In part (a), you have probably rejected the null hypothesis that the means for all four treatments are equal. However, the only meaningful way to decide which of the differences are significant is to either construct a confidence interval for each difference in means, or to conduct tests of hypotheses for every pair of group means. How many such tests would you need to perform for this experiment? (c) Using the Tukey-Kramer correction with a familywise confidence level of 95%, determine which treat- ment means are significantly different. Provide either p-values for all comparisons of pairs of means or the confidence intervals for the differences between all pairs of means to support your answer. (d) Based only on your work above (i.e. no additional work required), do you believe these data provide evidence that adding more N fertilizer increases lettuce yield? Briefly explain why or why not. (e) Using JMP or R, construct a linear trend contrast to test the null hypothesis of no linear trend in yield due to additional N fertilizer. Report the test statistic, p-value and conclusion for this test. 2 5. For an evaluation of diets used for routine maintenance of laboratory rats, researchers used a completely randomized design to allocate weanling male rats to five different diets (20 rats total). After four weeks, specimens of blood were collected and various biochemical variables were measured. We consider the results for blood urea concentration (mg/dl). The pooled standard deviation is 4.61 and the group means are as follows: Diet A B C D E Ȳ 40.0 40.7 32.9 29.6 48.8 A partial ANOVA table looks like: Source df RSS MS F Between diets 10.507 Within diets Total 1214.15 (a) Complete the ANOVA table above. What is the p-value for this test? Explain in a few words what your conclusion is based on this ANOVA table. (b) Construct a family of confidence intervals for the pairwise differences between Diet A and the other four diets. Use a method for determining significance that results in a familywise confidence level of at least 95%, for just this set of pairwise differences. Based on these intervals, which diets produce significantly different mean blood urea concentrations from Diet A? (c) Suppose Tukey’s minimum significant difference corresponding to 95% confidence is 8.55. Use this HSD to determine which pairs of means differ from one another in this problem. What can you conclude based on this analysis? Which Diet leads to the highest mean blood urea? Which leads to the smallest? Can you say anything about the order between the means? 3

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