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 miles per hour. The test was run on both dry and wet​ pavement, with results as shown below. Stopping Distance​ (ft) Wet 213 192 210 201 198 203 204 177 187 218 Dry 154 148 137 144 131 151 133 136 139 128 ​a) Construct a​ 95% confidence interval for the mean dry pavement stopping distance.

The confidence interval is

Answer 1

Sol:

For the given dry pavement sample

Dry 154 148 137 144 131 151 133 136 139 128

sample mean=xbar=1401/10=140.1

sample standard deviation=s=8.799621

sample size=n=10

alpha=1-0.95=0.05

alpha/2=0.05/2=0.025

df=n-1=10-1=9

t critical value in excel

==T.INV(0.025,9)

=2.262157163

95% confidence interval for mean is

xbar-t*s/sqrt(n),xbar+t*s/sqrt(n)

140.1-2.262157163*8.799621/sqrt(10),140.1+2.262157163*8.799621/sqrt(10)

133.8051, 146.3949

95% lower limit mean dry pavement stopping distance=133.8051

95% upper limit mean  dry pavement stopping distance.=146.3949