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#### Directions: answer all parts of questions 1 – 3 below

###### Statistics

Directions: answer all parts of questions 1 – 3 below. Then: 1. Write-up your answers in a Word document. 2. The scatterplots and residual plots requested for Questions 2 and 3 should be included in your write-up. 3. Attach the Word document and any supporting work to me

Background: you have been commissioned by Australian National Wildlife Federation (ANWF) to analyze several samples involving crocodiles. The included Excel spreadsheet contains:

• Sample 1 and Sample 2: length (in feet) measurements taken from two different coastal rivers. • Sample 3: age (in years) versus length (in feet) measurements of pre-adult crocodiles. • Sample 4: head length (HL, in feet) versus total length (TL, in feet) of mature crocodiles.

Questions:

1. The biologists who collected Sample 1 and Sample 2 are curious whether the two samples are of the same species of crocodile. One way to investigate this question would be to determine whether the samples come from populations with the same or different mean lengths Perform an appropriate hypothesis test at the .05 significance level to test the claim that the crocodiles in the two samples come from populations with different mean lengths. Make sure you explain your assumptions about the data, and report the value of the test statistic and the p-value for your test. What can you tell the biologists about the species of crocodiles in the samples?

2. The ANWF would like to have a model which predicts the approximate age of a pre-adult crocodile given its length. The data in Sample 3 relates the length and age measurements of a sample of pie-adult crocodiles caught and then released from various locations. a. Plot a scatterplot of the data. Is the scatterplot approximately linear? h. Assuming the answer to the second part of (a) is yes, perform an appropriate hypothesis test at the .05 significance level to test the claim that length and age are linearly related. Make sure to explain your assumptions about the data, and report the value of the test statistic and the p-value. State the decision (reject, fail to reject) and give a written conclusion that can explain the outcome of the test to a non-statistician. What are r and r2 for this data set?

d. What is the regression equation? e. Make a residual plot for this regression equation. f. Does the regression equation appear to be a good model for the data? Explain,  making sure to cite particulars from your analysis so far. g. Assuming the regression equation is a good model for the data, use it to predict the age of a pre-adult crocodile whose length is 10 feet.

3. Sample 4 relates head length (HL, in feet) and total length (TL, in feet) of another sample of crocodiles, also caught and released from various locations. a. Plot a scatterplot of the data. Is the scatterplot approximately linear? b. Assuming the answer to the second part of (a) is yes, perform an appropriate hypothesis test at the .05 significance level to test the claim that length and age are linearly related. Make sure to explain your assumptions about the data, and report the value of the test statistic and the p-value. State the decision (reject, fail to reject) and give a written conclusion that can explain the outcome of the test to a non-statistician. c. What are r and r2 for this data set? d. What is the regression equation? e. Make a residual plot for this regression equation. f. Does the regression equation appear to be a good model for the data? Explain,  making sure to cite particulars from your analysis so far. g. Consider the drone images of partially submerged crocodiles shown below:

Image 1

Image 2

Using external reference markers, it was possible to determine the head length of the crocodile shown in Image 1. Use your model to predict its total length. h. As in (g), an external marker was used to determine the head length of crocodile A in Image 2. What is your prediction for crocodile A's total length? i. In image 2, can crocodile B's total length be predicted? (Hint: there is no measurement given for B, but you do have a known length for A that could be used to approximate B's head length. But also think about the range of values your model can be applied to.) j. Can you think of any reason ANWF might want a model that predicts total length given head length? Explain.

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