In a test of braking performance, a tire manufacturer measured the stopping dist

Question

In a test of braking performance, a tire manufacturer measured the stopping distance for one of its tire models. On a test track, a car made repeated stops from 60 mph. The company tested the tires on 10 different cars, recording the stopping distance for each car on both dry and wet pavement, with the following results. car = 1:10 dist = c(150, 147, 136, 134, 130, 134, 134, 128, 136, 158, 201, 220, 192, 146, 182, 173, 202, 180, 192, 206) pavement = c(rep(' Dry', each = 10) rep('Wet', each = 10)) stop = data.frame (car, dist, pavement) (a) Estimate the true average difference of braking performance on wet vs. dry roads with 98% confidence. Interpret. (b) Is there a difference in the mean braking performance on wet vs. dry roads? Conduct hypothesis test. Let alpha = 0.02 (c) State the kind of error could have been made in context of the problem. (d) Now do part b again in R

Explanation / Answer

At first, we can load the data into R environment with the given commands:

car <- 1:10
dist <- c(150,147,136,134,130,134,134,128,136,158,201,
220,192,146,182,173,202,180,192,206)
pavement <- c(rep('Dry',each=10),rep('Wet',each=10))
stop <- data.frame(car,dist,pavement)

t test can be carried out in R using t.test() function.

First we can check for the assumption of constant variance in both groups using Levenes test as below:

library(car)
leveneTest(dist ~ pavement, data = stop)

Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 1 2.6602 0.1203
18   

Here we can see that the assumption of constant variance is not violated.

Now we can conduct the hypothesis test as below:

t.test(dist ~ pavement, data = stop, alternative = "two.sided", conf.level = 0.98, var.equal=T)

   Two Sample t-test

data: dist by pavement
t = -7.0501, df = 18, p-value = 1.412e-06
alternative hypothesis: true difference in means is not equal to 0
98 percent confidence interval:
-69.05526 -32.34474
sample estimates:
mean in group Dry mean in group Wet
138.7 189.4

As p value is less than 0.02, we can reject the null hypothesis. So there is difference in the braking performance on wet and dry roads.

98 percent confidence interval is:
-69.05526 -32.34474

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