4. In this exercise, we will examine two different varieties of wheat seeds: (1) Kama; and (2) Canadian. We are interested in the length. of the wheat kernel. We are going to use real data, available here: https://archive.ics.uci.edu/ml/datasets/seeds. Below is sample of size 30 of each wheat variety's mea- sured kernel length: - Kama: 5.717 5.712 5.351 5.832 5.226 5.395 5.139 5.384 5.877 5.388 5.386 5.008 5.397 4.902 5.789 5.662 5.656 5.585 5.609 5.504 5.618 5.099 5.757 5.479 5.554 5.579 5.527 5.520 5.701 5.630 - Canadian: 5.236 5.180 5.472 5.136 5.240 5.220 5.394 5.410 5.046 5.088 5.073 5.236 5.180 5.363 5.317 5.176 5.386 5.175 5.009 5.186 5.011 5.160 4.899 5.413 5.140 5.320 5.088 5.091 5.090 5.451 Before you answer the questions below, think about the following (no need to write it down): just by looking to these data, can you conclude which wheat variety has a longer kernel? Imagine if the sample were of size 1000? [No marks] (a) Find the average kernel length of each type of wheat. Based on these averages alone, can we claim that we know that Kama seeds have a longer true kernel average than Canadian seeds? Briey explain in 1 4 sentences why or why not. [2 marks] (b) Next, check how much the kernels' lengths vary - obtain the standard deviation for each type of wheat. [1 mark] (c) Find the standard error of the sample averages of each wheat type. [1 mark] (d) Obtain 99.7% confidence intervals for the population mean length of each wheat type. [4 marks] (e) Obtain a 95% confidence interval for the difference in true mean lengths between the two types of wheat. [2 marks] (f) Based on the interval you obtained in part (e), do the data suggest the true mean seed length is different for the two types of wheat? State your hypotheses (in words or define your notation) and conclusion in the context of the question. [3 marks]