Question

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. 41
C. The mean depth (in m) of all Northern Hemisphere icebergs.
D. The variance of the depths (in m22) of all Northern Hemisphere icebergs.
E. 20 meters
F. The mean depth (in m) of the 41 icebergs in the study.
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. fail to reject the null hypothesis at all.
D. reject the null hypothesis at ?=0.05α=0.05 level of significance
E. reject the null hypothesis at ?=0.1α=0.1 level of significance
F. None of the above

Answer 1

Part a)

Answers:
A) 270 meters
C) The mean depth (in m) of all Northern Hemisphere icebergs.

Part b) The null hypothesis is:
Answer: The mean depth of the Northern Hemisphere icebergs is 270 meters now.

Part c): The alternative hypothesis to be:
Answer: one-sided, right-tailed.

Part d):

Answer: There is sufficient evidence to suggest that the mean depth of Northern Hemisphere icebergs has increased due to global warming.

Part e):

Answer: It is certainly correct that the mean depth of Northern Hemisphere icebergs has increased due to global warming.

Part f)
Answer: there is a 4% chance that the mean depth of Northern Hemisphere icebergs has increased due to global warming.

Part g)

Answers: D) reject the null hypothesis at α=0.05 level of significance
                 E) Reject the null hypothesis at α=0.1 level of significance