A group of researchers wants to estimate the true mean skidding distance along a
ID: 3291746 • Letter: A
Question
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 at
2020
randomly selected road sites. These values are given in the accompanying table. Complete parts a through d.
489489
352352
455455
196196
290290
405405
575575
440440
546546
383383
295295
434434
183183
263263
274274
405405
315315
313313
142142
424424
a.
Estimate the true mean skidding distance for the road with a
9999%
confidence interval.
left parenthesis nothing comma nothing right parenthesis,
(Round to one decimal place as needed.)
b. Give a practical interpretation of the interval, part a.
The confidence interval means that we are
nothing%
confident that the true
skidding distance standard deviation
mean skidding distance
skidding distance variance
for
the whole road
the sampled points
is in the interval.
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 population distribution must be approximately normal.
C.
The sample must be randomly selected from the population.
D.
The sample must be selected carefully to represent the whole population.
Is it reasonable to assume that the population distribution is approximately normal?
A.
Yes, because the sample distribution is approximately normal.
B.
No, because the sample distribution is definitely not normal.
C.
The condition does not apply.
Is it reasonable to assume that the sample is random?
A.
The condition does not apply.
B.
No, because we do not know the methods used by the researchers.
C.
Yes, because the problem statement indicates that it is.
Is it reasonable to assume that the sample size is much smaller than the population size?
A.
No, because the length of the road is unknown.
B.
The condition does not apply.
C.
Yes, because there are many points that could be chosen along the road.
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.
No, because we do not know the methods used by the researchers.
C.
The condition does not apply.
d. A logger working on the road claims the mean skidding distance is at least
449449
meters. Do you agree?
No
Yes
, because the value
449449
lies
outside
inside
the confidence interval.
489489
352352
455455
196196
290290
405405
575575
440440
546546
383383
295295
434434
183183
263263
274274
405405
315315
313313
142142
424424
Explanation / Answer
for 99% interval ; t=2.8609
therefore 99% confidence interval =sample mean -/+ t*std error =283.7 ; 434.2
b) The confidence interval means that we are 99% confident that the true mean skidding distance for the whole road is in the interval
c)
B.
The population distribution must be approximately normal.
Is it reasonable to assume that the population distribution is approximately normal?
A.
Yes, because the sample distribution is approximately normal.
Is it reasonable to assume that the sample is random?
C.
Yes, because the problem statement indicates that it is.
Is it reasonable to assume that the sample size is much smaller than the population size?
C.
Yes, because there are many points that could be chosen along the road.
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.
d)
No
because the value 449 lies outside the confidence interval.
X 489 352 455 196 290 405 575 440 546 383 295 434 183 263 274 405 315 313 142 424 mean(X) 358.9500 std deviation(S) 117.6509 std error =S/(n)1/2 26.3075Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.