Question

(7 pts) 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) What is/are the parameters of interest relevant to this hypothesis test? Choose all parameters that you use to set up the null and alternative hypotheses, as well as those referenced in the assumptions and derivation of the relevant test statistic.
A. 41
B. 270 meters
C. The mean depth (in m) of the 41 icebergs in the study.
D. The mean depth (in m) of all Northern Hemisphere icebergs.
E. 20 meters
F. The variance of the depths (in m2 ) 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?
A. The mean depth of the Northern Hemisphere icebergs is smaller than 270 meters now.
B. The mean depth of the Northern Hemisphere icebergs is greater than 270 meters now.
C. The mean depth of the Northern Hemisphere icebergs used to be smaller than 270 meters.
D. The mean depth of the Northern Hemisphere icebergs is 270 meters now.
E. The mean depth of the Northern Hemisphere icebergs used to be 270 meters.
F. The mean depth of the Northern Hemisphere icebergs is different from 270 meters now.
G. The mean depth of the Northern Hemisphere icebergs used to be different from 270 meters.
H. The mean depth of the Northern Hemisphere icebergs used to be greater than 270 meters.

Part c) You would take the alternative hypothesis to be:
A. two-sided.
B. one-sided, right-tailed.
C. one-sided, left-tailed
D. 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?
A. There is insufficient evidence to suggest that the mean depth of the Northern Hemisphere icebergs has not changed.
B. There is insufficient evidence to suggest that the mean depth of Northern Hemisphere icebergs has increased due to global warming.
C. There is sufficient evidence to suggest that the mean depth of Northern Hemisphere icebergs has decreased due to global warming.
D. There is insufficient evidence to suggest that the mean depth of Northern Hemisphere icebergs has decreased due to global warming.
E. There is sufficient evidence to suggest that the mean depth of Northern Hemisphere icebergs has increased due to global warming.
F. There is sufficient evidence to suggest that the mean depth of the Northern Hemisphere icebergs has not changed.

Part e) Suppose that, based on data collected, you decide that the mean depth of Northern Hemisphere icebergs has increased due to global warming.
A. it is certainly incorrect that the mean depth of Northern Hemisphere icebergs has increased due to global warming.
B. it is certainly correct that the mean depth of Northern Hemisphere icebergs has increased due to global warming.
C. there must have been a problem with the way the sample was obtained.
D. it is possible that you are making a Type II error.
E. it is possible that you are making a Type I error.

Part f) Suppose that, based on the data collected, you obtain a P -value of 0.04. This means:
A. 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.
B. 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.
C. there is a 4% chance that the mean depth of Northern Hemisphere icebergs has decreased due to global warming.
D. the sample of icebergs are relatively smaller in depth, if indeed the true mean depth of the Northern Hemisphere icebergs is 270 meters now.
E. there is a 4% chance that the mean depth of Northern Hemisphere icebergs has increased due to global warming.
F. the sample of icebergs are relatively greater 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. neither reject nor accept the null hypothesis.
B. fail to reject the null hypothesis at all.
C. reject the null hypothesis at α=0.1 level of significance
D. reject the null hypothesis at α=0.05 level of significance
E. believe the null hypothesis is true.
F. None of the above

Answer 1

PART A.

The parameters we need are

C. The mean depth (in m) of the 41 icebergs in the study.

D. The mean depth (in m) of all Northern Hemisphere icebergs.

F. The variance of the depths (in m2 ) of all Northern Hemisphere icebergs.

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PART B.

D. The mean depth of the Northern Hemisphere icebergs is 270 meters now.

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PART C.

B. one-sided, right-tailed.

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PART D.

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

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