can you help me

The Iris flower dataset was introduced by the famous British statistician Ronald Fisher. The dataset originally contains n = 50 samples from each of three species of Iris (Iris setosa, Iris virginica and Iris versicolor). For each species, the length and the width (in centimeters) of the sepals and petals are measured. We here analyse one of the flower species, Iris virginica, and we focus on a single variable X, which is the sepal width of Iris virginica. For the n = 50 Iris virginica flowers, the following statistics are obtained )_ TI = 148.7 and (71 - 2) = 5.0962. Moreover, an exploratory analysis shows that you may assume a normal population for the sepal width of Iris virginica. No previous studies are available to you, so you may not assume that the population variance is known. (a.) (1 mark) Propose an unbiased estimator for the population mean of the sepal width of Iris virginica. Report the estimate given the data above.(b.) (2 marks) What is the sampling distribution of your proposed estimator in (a.)? Carefully state your assumptions. (c.) (1 mark) Propose an unbiased estimator for the population variance of the sepal width of Iris virginica. Report the estimate given the data above. (d.) (2 marks) What is the sampling distribution of your proposed estimator in (c.)? Carefully state your assumptions. Hint: We have not directly encountered the sampling distribution of the estimator in (c.). However, we have encountered the sampling distribution of a properly scaled version of the estimator many times. Report the sampling distribution of this scaled estimator instead. (e.) (2 marks) A botanist says that she wants a two-sided 95% confidence interval of the population variance of the sepal width of Iris virginica. Provide such an interval to the botanist and interpret it. Use the closest available approximation when reading the relevant quantiles from the statistical tables in the textbook. Alternatively, you may compute exact quantiles using R. (f.) (2 marks) The botanist says that she plans to pluck a single Iris virginica tomorrow. Provide an appropriate two-sided 95% interval that provides information about the sepal width of the flower she will pluck. Use the closest available approximation when reading the relevant quantiles from the statistical tables in the textbook. Alternatively, you may compute exact quantiles using R