Reference materials;

ducks.mwx

Question 5 11 marks (8) Using Minitab, or otherwise, produce a diagram containing boxplots of the weights for the hatchyear ducks and the weights of the adults. (These weights are given in separate columns, hatch-year and adult, of the le duck weightsmwx.) Ensure that the boxplots are horizontal, have the same scale and are drawn on one diagram. Prepare these boxplots ready for inclusion in a report by ensuring that the title and the horizontal axis label are clear and informative. Include the nished boxplots in your answer. Complete the following table of summary statistics for the weights of ducks. (All the values should be rounded to the nearest whole number.) Table 2 Hatchyear ducks Adult ducks Number Mean Median Standard deviation Interquartile range Range Using your answer to part (a), compare the skewness of the distribution of weights of hatchyear ducks to the skewness of the distribution of weights of adult ducks. Using your answer to part (b), calculate by hand the estimated standard error for the mean weight of hatchyear ducks. Show your working and give your answer to one decimal place. Question 6 14 marks In Question 5, you compared the distributions of weights of hatchyear and adult ducks. In this question you will consider one aspect of the distribution the mean weight. Suppose now that interest focuses on whether the population mean weight of ducks is the same for hatchyear and adult ducks. (8) (13} write down suitable null and alternative hypotheses, stating clearly the meaning of any symbols that you use. In part (d), you will use a twosample ttest to test the hypotheses that you wrote down in part (a), using the data in duck weights.mwx. Explain why neither the twosample ztest nor the paired ttest would be suitable for these data. For the data in duck weights.rnwx, is the assumption of a common population variance reasonable? Justify your opinion. State any other assumptions that are made about the data. [2] [4] (d) Use the twosample ttest to test the hypotheses that you wrote down in part (a). (Whatever answer you gave in part (c), you should assume that the assumption of a common population variance is indeed reasonable, along with any other necessary assumptions.) In your answer, make sure to include: o the value of the pooled estimate of the common standard deviation 0 the value of the test statistic o the degrees of freedom 9 the pvalue, or the values of CV5 and CV1 9 any conclusions that can be drawn from the results of this test. Question? 3marks Suppose that the original researchers were interested in taking more detailed measurements of the ducks that. were initially captured, but could afford to do this with only 5 of the 50 ducks. Using simple random sampling, select a sample that the researchers could have used. To help you to select this sample, you may use either Minitab or the random number table given in the appendix to Unit 4. In your answer, you should outline the method that you used to obtain the sample, and detail which random numbers you generate (including any that you discard). If you use Minitab, then you should make sure that the seed of the random number generator is initially set to take the value 1058. If you use the random number table, then you should start at row 8. QuestionB 3marks A different researcher would like to test a new treatment for seabirds that get contaminated after an oil spill. rIl'he next time there is an oil spill, she proposes taking pairs of birds and using this new treatment on one bird in each pair and applying a standard treatment to the other. The outcome is then whether or not each bird is t enough to be released back into the wild. (a) Explain why the data from this trial would be regarded as objective data. (b) Explain why the data from this trial relating to each bird would be regarded as categorical data. (c) How should the pairs of birds be selected to ensure that this is a matchedpairs trial