Reference materials;

ducks.mwx

In this EMA, you will analyse some data on the survival times of ducks described below. Some female ducks, taken from two locations in New Jersey, were captured and tted with radios over a period of about one month, starting in midNovember one particular year. Their progress was then closely monitored until late February the following year, when the experiment was terminated. Eighteen birds died eight from natural causes and ten due to hunters. The hunting season ended in midFebruary. The survival time is either the time until death or the time up to the end of the period of observation. [Data source: Pollock, K.H., W'interstein, S.R. and Conroy, M..I. (1989) 'Estimation and analysis of survival distributions for radiotagged animals\Question3 18 marks Using the data given in ducks.mvvx, a researcher wishes to construct a model to predict the winglength of a duck based on its weight. (a) Briey explain why the researcher should treat weight as an explanatory variable and winglength as a dependent variable. (b) Obtain a scatterplot of winglength against weight. Include this scatterplot in your answer. Interpret this scatterplot, giving reasons for your interpretation. (c) What is the equation of the least squares regression line tted to these data? With reference to a suitable residual plot (which you should include in your answer), briey discuss whether or not the least squares regression line ts the data well. (d) Using the line tted in part (c), predict the winglength of a duck that weighs 1200 g. Also state the 95% prediction interval for the winglength of a duck that weighs 1200 g. Give both of your answers rounded to the nearest whole number. Interpret the prediction interval. Question4 13 marks A contingency table of the age of the ducks and whether or not their deaths had been observed is given below. Table 1 Age Hatchyear duck Adult duck Total Death not observed 19 13 32 Death observed 12 6 18 Total 31 19 50 Note that this table is given in the le duck death.mwx. (a) Explain carefully why this table is correctly described as a contingency table. (b) What is the probability that a randomly selected duck from this group was observed to have died? Give your answer to three decimal places. (c) What is the probability that a randomly selected duck from this group was observed to have died given that it was a hatchyear duck? Give your answer to three decimal places. (d) Suppose that a researcher is interested in the following question: Does the age of a duck aect whether or act the death of the deck was observed? (i) 'Write down suitable null and alternative hypotheses. (ii) Using the X2 test for contingency tables, test the hypotheses you wrote down in part (d)(i). Make sure to include in your answer: 0 a table of the expected values (with the expected values given to two decimal places) the value of the test statistic the degrees of freedom the pvalue, or the values of CV5 and CV1 your conclusion from the test. [9] [4] [3] [6]