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 h) Suppose that, based on data collected, you reject the null hypothesis. Which of the following could you conclude?
A. There is sufficient evidence to suggest that the mean depth of Northern Hemisphere icebergs has increased due to global warming.
B. There is sufficient evidence to suggest that the mean depth of the Northern Hemisphere icebergs has not changed.
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 the Northern Hemisphere icebergs has not changed.
E. There is insufficient evidence to suggest that the mean depth of Northern Hemisphere icebergs has increased due to global warming.
F. There is insufficient evidence to suggest that the mean depth of Northern Hemisphere icebergs has decreased due to global warming.

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

Answer 1

The Hypothesis:

H0: = 270

Ha: > 270

This is a right tailed test

The Test Statistic: The test statistic is given by the equation:

The p value (Right tailed) at t (1.92, df = 40) = 0.0310

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If We reject the data, then Option A: There is sufficient evidence to conclude that the mean depth of Northern Hemisphere icebergs has increased due to global warming.

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If we decide that The depth has increased, this is basis the fact that at an level of 0.05, this would be correct, but at an level of 0.01, this would be rejected.. Hence I might be failing to reject a false null hypothesis.

Therefore Option B: It is possible you are making a Type II error.

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