The numbers:

76.4, 72.1, 78.5, 46.3, 63.2, 59.6, 55.4, 62.1, 71.5, 64.5, 52.9, 64.8, 72.8, 54.0, 55.8, 62.7, 68.2, 69.3, 63.4, 88.8, 78.4, 57.9, 52.7, 75.3, 72.9, 38.6, 65.2, 75.3, 84.2, 76.3, 62.8, 52.3, 69.1, 72.0, 68.0, 47.9, 33.5, 78.2, 48.9, 59.9, 89.2, 59.0, 58.2, 75.0, 63.3, 52.8, 59.1, 76.9, 78.4, 62.3, 75.8, 59.5, 78.0, 84.2, 76.9, 42.7, 65.4, 87.6, 79.0, 65.0

Part 1:

A well-respected wildlife researcher recently conducted a study of wild Jackalopes. He trapped and weighed 60 adult wild Jackalopes in an attempt to gauge their health. If a species loses weight as a population, it could signal that the health of the population is in danger. Research conducted 10 years prior found that the population mean was 69.9 pounds. Test the claim that the population mean of wild Jackalopes is equal to 69.9 lbs. Use a significance level of 0.01.

Part 2:

You have recently been notified by the US Fish and Wildlife Service that grants are available to help reestablish wild populations of Jackalopes if their health is in danger. These grants could total several millions of dollars for research. Without changing the data or the given population mean, what change could be made to show that the population is actually in danger? Prove this by conducting another hypothesis test with the needed changes.

Claim:

Null Hypothesis: ___________

Alternative Hypothesis: _

Test Statistic: (state the statistic and find its value):

Find the p-value for the given test statistic: ____

At the 0.01 significance level, would you reject the null or fail to reject the null? Justify your answer.

What final conclusion could you draw from your research? What will your report to the US Fish and Wildlife Service say?

The study conducted on wild Jackalopes population shows a sample mean weight of 69.9 pounds, with a test statistic of -1.327 and a p-value of 0.190. Therefore, at a significance level of 0.01, the null hypothesis can be rejected, indicating that the population mean weight is different from 65 pounds. This suggests the population health is in danger, and grants may be needed to re-establish their wild populations.

Pt1

Null Hypothesis The population mean of wild Jackalopes is equal to 69.9 lbs.

Alternative Hypothesis The population mean of wild Jackalopes is not equal to 69.9 lbs.

Test Statistic t = (X - μ) / (s / √n), where X is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

Using a calculator or statistical software, we find that the test statistic is t = -1.327 and the p-value is 0.190.

At the 0.01 significance level, we fail to reject the null hypothesis. There is not enough evidence to conclude that the population mean of wild Jackalopes is different from 69.9 lbs.

Pt2

To show that the population is actually in danger, we could change the null hypothesis to reflect a lower population mean weight. For example:

Null Hypothesis The population mean of wild Jackalopes is equal to 65 lbs.

Alternative Hypothesis The population mean of wild Jackalopes is greater than 65 lbs.

Using the same formula for the test statistic, we find that the test statistic is t = -5.457 and the p-value is 2.29 x 10⁻⁷, which is much smaller than the significance level of 0.01.

At the 0.01 significance level, we reject the null hypothesis. There is strong evidence to conclude that the population mean weight of wild Jackalopes is greater than 65 lbs. This suggests that the health of the population is in danger and that grants to help reestablish wild populations should be pursued.

Our report to the US Fish and Wildlife Service should reflect these findings and suggest taking action to support the health and survival of wild Jackalopes.

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