# Compute and normal-plot residuals as a crude means of investigating

**Question description**

1. In an ISU engineering research project, so called "tilttable tests" were done in order to determine the angles at which vehicles experience lift-off of the "high-side" wheels and begin to roll over. So called "tilttable ratios"(which are the tangents of angles at which lift-off occurs) were measured for four different vans with the following results:

Van#1 - 1.096, 1.093, 1.090, 1.093

Van#2 - .962, .970, .967, .966

Van#3 - 1.010, 1.024, 1.021, 1.020, 1.022

Van#4 - 1.002, 1.001, 1.002, 1.004

(notice that Van#3 was tested 5 times while the others were tested four times each.) Vans#1 and #2 were minivans and Vans#3 and #4 were full-sized vans.

(a) Compute and normal-plot residuals as a crude means of investigating the appropriateness of the one-way model assumptions for tilttable ratios. Comment on the appearance of your plot.

(b) Compute pooled estimate of the standard deviation based on these four samples. What is Sp suppose to be measuring in this example? Give a two-sided 95% confidence interval for sigma (Ơ) based on Sp.

(c) Individual confidence intervals for the differences between particular pairs of mean tilttable ratios are of the form ӯi - ӯi’ +- ∆ for appropriate vales of ∆. Find values of ∆ if individual 99% two sided intervals are desired, first for pairs of means with samples of sieze 4 and then for pairs of means where one sample size is 4 and the other is 5.

(d) It might be of interest to compare the average of the tilttable ratios for the minivans to that of the full-size vans. Give a 99% two-sided confidence interval for the quantity 0.5(**μ**1 + **μ**2) - 0.5(**μ**3 + **μ**4).

(e) make an ANOVA table for the data then find both R^2 for the one-way model and also the observed level of significance for an F test of the null hypothesis that all four vans have the same mean tilttable ratio.

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