Question

OFultos The data suggests that the omerence between mean stopping dstances is less than t -10. table in the Appendix of Tables to answer this question r-1292, and "i-S59. Caarate·95% a for th, diference between trn overage stopping estances for cas oped with system i and cars eg pped wen system 2 (Round your answers to deow places. 》 -21 70

Answer 1

We have to test (Left tailed T-test)

$H_0:\mu _1-\mu _2=-10\\ H_1:\mu _1-\mu _2 < -10$

The sample means are $\overline{x}=115.2, \overline{y}=129.6$ . The sample standard deviations are s . Sample sizes are   $n_1=7,n_2=7$
The estimated mean difference is $\overline{x}-\overline{y}=-14.4$
We use T distribution since the sample sizes are small. The test statistic

$t=\left (\overline{x}-\overline{y} +10\right )/\sqrt{\frac{s _1^2}{n_1}+\frac{s _2^2}{n_2}}\\ {\color{Blue} t=-1.58}$

The statistic follows T-distribution.

The P-value is $P\left ( T<t \right )=P\left (T<-1.58\right )={\color{Blue} 0.070}$

Sinc the P-value $\textup{P-value} = 0.07>\alpha =0.01$   we retain retain the null hypothesis

Fail to reject the null hypothesis.

We are required to solve only one question. Please post the remaining questions as another post.