Question 4 [1+3+1+2+1 = 8 marks] In 2018, the proportion of penguin nesting locations within the Lillico Beach, Tasmania, area was found to be: Table 1. Penguin nesting locations within the Lillico Beach, TAS, area. Proportion of nests marina 11% bay 17% beach 28% headland 44% In 2023 an environment committee of the Lillico Beach local government was interested in using this historical data to help determine if a recent large-scale development had changed the proportion of penguin nesting locations. The committee commissioned a study that counted penguin nests in 2023 across the same areas. Observations are shown in Table 2. Table 2. Number of Penguin nests at nesting locations within the Lillico Beach, TAS, area. marina Number of nests 9 bay 18 beach 67 Consider the information above and answer the following. headland 86 (a) What are the degrees of freedom for this Chi-square goodness of fit test? (b) Calculate the x test statistic. (c) Calculate the Critical Chi-squared value at a significance level of 0.05 (please state the Excel formula used)? (d) What decision can be made regarding the null hypothesis? Please provide a reason for your answer and state the decision rule used. (e) What conclusion could be made in relation to the proportions of penguin nesting locations within the Lillico Beach, Tasmania, area?