A study was conducted to test the effect of a new ecofriendl

A study was conducted to test the effect of a new ecofriendly alternative to road salt on automobile traction. A random sample of the skidding distance (in meters) of cars along the same stretch of highway during a cold, icy winter day was obtained. The data are given in the following table.

488

352

455

199

288

406

575

435

545

385

299

433

183

260

273

402

310

313

143

424

Suppose the distribution of skidding distances is normal. Find a 95% confidence interval for the true mean skidding distance.

Solution

sample mean=358.4

sample standard deviation =117.19278

sample size n=20

The degree of freedom =n-1=20-1=19

Given a=0.05, t(0.025, df=19) =2.09 (from student t table)

So a 95% confidence interval for the true mean skidding distance is

xbar +/- t*s/vn

--> 358.4 +/- 2.09*117.19278/sqrt(20)

--> (303.6313, 413.1687)