In: Statistics and Probability
From previous studies, it has been generally believed that Northern Hemisphere icebergs have a mean depth of 270 meters and a standard deviation of 20 meters. An environmentalist has suggested that global warming has caused icebergs to have greater depth. A team of scientists visiting the Northern Hemisphere observed a random sample of 41 icebergs. The depth of the base of the iceberg below the surface was carefully measured for each and the sample mean and standard deviation were calculated.
Part a) Which of the following is/are parameter(s) of interest with respect to the new investigation here? (Select all that apply)
A. 270 meters
B. The variance of the depths (in m22) of all
Northern Hemisphere icebergs.
C. 41
D. 20 meters
E. The mean depth (in m) of the 41 icebergs in the
study.
F. The mean depth (in m) of all Northern
Hemisphere icebergs.
G. None of the above
Part b) In testing a hypothesis about a parameter of interest, what would your null hypothesis be?
The mean depth of the Northern Hemisphere icebergs is 270 meters
now.
The mean depth of the Northern Hemisphere icebergs is greater than
270 meters now.
The mean depth of the Northern Hemisphere icebergs is smaller than
270 meters now.
The mean depth of the Northern Hemisphere icebergs is different
from 270 meters now.
The mean depth of the Northern Hemisphere icebergs used to be 270
meters.
The mean depth of the Northern Hemisphere icebergs used to be
greater than 270 meters.
The mean depth of the Northern Hemisphere icebergs used to be
smaller than 270 meters.
The mean depth of the Northern Hemisphere icebergs used to be
different from 270 meters.
Part c) You would take the alternative hypothesis to be:
one-sided, right-tailed.
two-sided.
one-sided, left-tailed
it does not matter whether we take a one-sided or two-sided
alternative.
Part d) Suppose that, based on data collected, you reject the null hypothesis. Which of the following could you conclude?
There is sufficient evidence to suggest that the mean depth of
Northern Hemisphere icebergs has increased due to global
warming.
There is sufficient evidence to suggest that the mean depth of the
Northern Hemisphere icebergs has not changed.
There is sufficient evidence to suggest that the mean depth of
Northern Hemisphere icebergs has decreased due to global
warming.
There is insufficient evidence to suggest that the mean depth of
the Northern Hemisphere icebergs has not changed.
There is insufficient evidence to suggest that the mean depth of
Northern Hemisphere icebergs has increased due to global
warming.
There is insufficient evidence to suggest that the mean depth of
Northern Hemisphere icebergs has decreased due to global
warming.
Part e) Suppose that, based on data collected, you decide that the mean depth of Northern Hemisphere icebergs has increased due to global warming.
it is possible that you are making a Type I error.
it is possible that you are making a Type II error.
it is certainly correct that the mean depth of Northern Hemisphere
icebergs has increased due to global warming.
it is certainly incorrect that the mean depth of Northern
Hemisphere icebergs has increased due to global warming.
there must have been a problem with the way the sample was
obtained.
Part f) Suppose that, based on the data
collected, you obtain a ?P-value of 0.04. This means:
the sample of icebergs are relatively greater in depth, if indeed
the true mean depth of the Northern Hemisphere icebergs is 270
meters now.
there is a 4% chance that the mean depth of Northern Hemisphere
icebergs has increased due to global warming.
there is a 4% chance that the mean depth of Northern Hemisphere
icebergs has decreased due to global warming.
the probability of the mean depth of icebergs measuring 270 meters,
or greater is 0.04, if indeed the true mean depth of the Northern
Hemisphere icebergs is 270 meters now.
the probability of the mean depth of icebergs measuring 270 meters,
or smaller is 0.04, if indeed the true mean depth of the Northern
Hemisphere icebergs is 270 meters now.
the sample of icebergs are relatively smaller in depth, if indeed
the true mean depth of the Northern Hemisphere icebergs is 270
meters now.
Part g) Based on the ?P-value that was
obtained, you would (Select all that apply):
A. believe the null hypothesis is true.
B. neither reject nor accept the null
hypothesis.
C. reject the null hypothesis at ?=0.05α=0.05
level of significance
D. fail to reject the null hypothesis at
all.
E. reject the null hypothesis at ?=0.1α=0.1 level
of significance
F. None of the above