Reference no: EM132251122

Questions -

Q1. An insurance company is concerned that garage A is charging too much for repairing damage to cars. Ten damaged cars were taken to both garage A and another garage (garage B) for estimates. The table below shows the estimates for repairing the cars (in dollars).

Repair Estimate

(a) State the null and alternate hypotheses.

(b) Is there significant evidence that the mean repair estimate of Garage A is higher than the mean repair estimate of Garage B(using an appropriate t-test)? Use α = 0.01 as the level of significance. Explain your answer. What is the p-value?

(c) Do the conditions required for using the t procedures appear to be valid for these data? Justify your answer.

(d) Find a 99% confidence interval of the mean difference in the average repair estimate between the two garages.

(e) According to the confidence interval, would it be reasonable to say that, on average, the Garage A estimate is at least $300 more than the Garage B estimate?

Q2. A clinical study is designed to assess differences in albumin levels in adults following diets containing different amounts of protein. Low protein diets are often prescribed for patients with kidney failure. Albumin is the most abundant protein in blood, and its concentration in the serum is measured in grams per deciliter (g/dL). Clinically, serum albumin concentrations are used to assess whether patients have sufficient protein in their diets. Three diets are compared, ranging from 5% to 15% protein, with the 15% protein diet representing a typical American diet. The albumin levels of participants following each diet are shown below.

Is there is a significant difference in serum albumin levels among subjects on the three different diets? For reference, normal albumin levels are generally between 3.4 and 5.4 g/dL. By inspection, it appears that participants following the 15% protein diet have higher albumin levels than those following the 5% protein diet. The issue is whether this observed difference is statistically significant. Use α = .05 level of significance.

(a) State the null and alternate hypotheses.

(b) Conduct an AOV to test whether there is a difference in the mean albumin levels. State your conclusions.

(c) Test the hypothesis that the variances of the three populations are equal. State your conclusions.

(d) Is AOV appropriate for this experiment? State all the reasons.

(e) Conduct a Kruskal-Wallis test to determine whether there is a shift in distribution of albumin levels for the three groups. Is the conclusion reached using the Kruskal-Wallis test consistent with the conclusion reached in (b)? Explain.

(f) Conduct a multiple comparison procedure using DSCF option. Explain the conclusions.

(g) Suppose that the albumin level for the second patient under "15% Protein" was 9.5 rather than 6.5. Change the value in the EXCEL Spreadsheet to reflect this correction. Run the AOV and Kruskal-Wallis test with 6.5 replaced with 9.5. What happens to AOV test? What happens to Kruskal-Wallis test?

(h) Discuss the effect that an extreme value can have on AOV and Kruskal-Wallis tests.

(i) Use PROC FORMAT to decode Treatment names.

Q3. Write a SAS program to calculate the rank of all twelve albumin levels (described in Q2) from lowest to highest. And then sum the ranks for each diet group.

(a) What is the sum of ranks for the 15%-Protein diet group?

(b) What is the sum of all ranks across all diet groups?

Note - Include the SAS code that was required to do the statistical analysis in a separate page. Only include the SAS outputs that are needed for the above analyses. Do not include all the SAS outputs. You will parse through the SAS outputs for significant tests, p-values, boxplots, etc. to answer the questions.