A group of researchers wants to estimate the true mean skidding distance along a new road in a certain forest. The skidding distances (in meters) were measured at20 randomly selected road sites. These values are given in the accompanying table. Complete parts a through d.

490

347

455

198

287

408

573

438

548

384

298

430

184

261

273

404

312

310

144

423

a. Estimate the true mean skidding distance for the road with a % 90 confidence interval.

(?, ?) (Round to one decimal place as needed.)

c. What conditions are required for the inference, part b, to be valid? Are these conditions reasonably satisfied? Check all correct statements below.

A. The sample size must be much smaller than the population size.

B. The sample must be selected carefully to represent the whole population.

C. The population distribution must be approximately normal.

D. The sample must be randomly selected from the population.

Is it reasonable to assume that the population distribution is approximately normal?

A. The condition does not apply.

B. No, because the sample distribution is definitely not normal.

C. Yes, because the sample distribution is approximately normal.

Is it reasonable to assume that the sample is random?

A. Yes, because the problem statement indicates that it is.

B. The condition does not apply.

C. No, because we do not know the methods used by the researchers.

Is it reasonable to assume that the sample size is much smaller than the population size?

A. The condition does not apply.

B. Yes, because there are many points that could be chosen along the road.

C. No, because the length of the road is unknown.

Is it reasonable to assume that the sample was selected carefully to represent the whole population?

A. Yes, because the problem statement indicates that it was.

B. The condition does not apply.

C. No, because we do not know the methods used by the researchers.