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(13 marks) A consumer organization investigates the absorbency of two brands of paper towels, Brand A and Brand B. In particular, they take 25 sheets (of the same size) of each brand and measure the mass (in grams) of each. Next, they place each sheet on a wet surface for 30 seconds. They then re-measure the mass (in grams) of each sheet. Let no i = 1, .25. be the change in mass of (Le, the amount of water absorbed by) the im sheet of Brand A. Likewise, let Far, 12 = 1, ,25, be the change in mass of the im sheet of Brand B. Also, let d: = mg - Jim, r' = 1, ,25. Some summary statistics are as follows: Sample mean of water absorbed (Brand A) Sample mean of water absorbed (Brand B) Sample SI} of water 3.4 = 0.15 absorbed (Brand A) Sample SI} of water 3 = 0.12 absorbed (Brand B) Sample mean of differences of = 1.85 of water absorbed Sample SI} of differences of 3o = 0.14 water absorbed Of interest is whether the mean absorbencies of the two brands differ. They wish to conduct a hypothesis test at the 5% signicance level. a} (3 marks} State the three assumptions required for your test to be valid. b} (2 marks} What are the null and alternative hypotheses? c} (3 marks} What is the value of the observed test statistic? d} (1 mark) What is the distribution of the test statistic under the null hypothesis? e} (2 marks} Pretend that the observed test statistic is 2.61. What is the p-value? f} (2 marks} Pretend that the p-value is [1.029. State your conclusions in the language of the