Part 3 [6 marks] Suppose that we want to compare the protein content of carrageen moss ( Chondrus crispus), a species of red algae, from a population grown in North Bay, versus a population grown in South Bay. We test 26 samples of the algae from North Bay and 22 from the South Bay, and find the following protein contents (in g/100g dry weight): North Bay: 28.6 27.2 29.9 28.0 26.3 28.6 28.4 27.3 30.2 30.2 29.3 28.5 27.9 28.1 28.7 26.7 27.9 28.9 28.9 27.7 27.8 29.5 26.5 30.2 27.5 27.3 South Bay: 27.3 28.0 27.7 24.6 25.0 27.9 28.8 26.6 25.7 28.1 30.2 27.1 26.7 27.0 27.6 29.5 26.1 25.7 26.3 27.0 27.0 26.3 Note: These observations are also available as single rows in a text file (algaeData. txt) on Crowdmark, if you wish to make use of the scan () function along with the copy and paste capabilities on your computer. (a) Store the data for the samples in two appropriately named vectors. Calculate the sample standard deviations of the two groups. Copy and paste your commands and output for the standard deviations into your document. (You don't need to copy /paste the commands for creating the vectors). (b) Determine if you can assume the variances are equal between the two groups. Complete the necessary calculation in R, and then copy and paste the ratio of the standard deviations into your document. What do you assume about the variances? (c) Test the research hypothesis that the mean protein content of the two populations is not equal. Copy and paste the appropriate R command and output into your document.(d) Clearly state the p-value you found from part (c). What is the strength of the evidence against Ho? (e) Write a sentence stating your conclusion of the hypothesis test you just performed; that is, write your conclusion regarding the difference in protein content between the carrageen moss grown in North Bay vs South Bay. (f) Calculate a 90% confidence interval (i.e. a two-sided confidence interval) for the mean sound pressure of the new model of motor. Copy and paste the appropriate R command and output. In an additional line, clearly state the values you get for the confidence interval from your output