Question

From previous studies, it has been generally believed that Northern Hemisphere icebergs have a mean depth of 270 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. The sample mean and standard deviation were calculated to be 276 meters and 20 meters respectively.

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. Note that a parameter and the value of a parameter are not the same thing.

A. 270 meters
B. 41
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. 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) Compute the test statistic (Please round your answer to three decimal places):

Answer 1

(a) The parameters of Interest are

A - 270m (which is the average depth of all Icebergs in the Northern Hemisphere)

D - the mean depth (in m ) of all Northern Hemisphere Icebergs

_____________

(b) The Null Hypothesis Option 1: The mean depth of the Northern Hemisphere Icebergs is 270m now.

The Alternative Hypothesis would be Option 1: One sided, right tailed.

_____________

(c) The Test Statistic: Since the population standard deviation is unknown we use the students t test.

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(d) The test statistic is given by the equation:

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