When planning for a new forest road to be used for tree harv

When planning for a new forest road to be used for tree harvesting, planners must select the location to minimize tractor skidding distance. The skidding distances (in meters) were measured at 20 randomly selected road sites. The data arc given below. A logger working on the road claims the mean skidding distance is at least 404 meters. Is there sufficient evidence to refute this claim? Use alpha=0.05. 406 430 442 570 282 549 451 483 200 352 385 291 190 263 271 396 312 305 143 428 Choose the correct answer below. A. Do not reject the claim. There is sufficient evidence to indicate that Mu

Solution

sample mean=357.45

sample standard deviation =116.6513

Let mu be the population mean

Ho: mu= 404 (i.e. null hypothesis)

Ha: mu<404 (i.e. alternative hypothesis)

The test statistic is

t=(xbar-mu)/(s/vn)

=(357.45-404)/(116.6513/sqrt(20))

=-1.78

It is left-tailed test.

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

Given a=0.05, the critical value is t(0.05, df=19) =-1.73 (from student t table)

Since t=-1.78 is less than -1.73, we reject Ho.

Answer: C