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): equation editor

Part e) Assume all necessary conditions are met (random sampling, independence samples, large enough sample size). Which of the following approximate the sampling distribution of the test statistic in part d:

A. Normal distribution

B. t-distribution

Part f) In which of the following ranges must the P-value must lie?[You will need the t-table to answer this question.]

A. <0.005

B. 0.05-0.01

C. 0.01-0.025

D. 0.025-0.05

E. 0.05-0.10

F. >0.10

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. believe the null hypothesis is true.

D. reject the null hypothesis at ?=0.05 level of significance

E. reject the null hypothesis at ?=0.1 level of significance

F. None of the above

Part h) 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 i) 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.

Answer 1

Solution1:

sample is a subset of population

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

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

Soluton2:

Null hypothesis :

H0:mu=270

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

Solution3:

H1:mu>270

From words:

suggested that global warming has caused icebergs to have greater depth

right-tailed.

Solutiond:

Compute the test statistic

t=sample mean-pop mean/samplesd/sqrt(n)

=276-270/20/sqrt(41)

t=1.921

test statistic is 1.921