6. A group of university students collect a random sample of 10 cans of White Lightning Cola from stores around Sweden. According to the packaging, each container is supposed to contain 330 ml of soda. The amount of soda, measured in milliliters, in each of the 10 cans can be found in the table below: 1 2 3 4 5 6 8 9 10 volume 331 329 328 328 328 329 331 329 328 329 a) Find the sample mean and sample variance of the sample. Remember to show your work! (5p Test at a 10% level of significance whether the mean content of a can of White Lightning Cola is less than 330 ml. Assume that the amount of soda in a randomly selected can is normally distributed. b) State necessary assumptions, hypotheses and the test variable. (5p) c) State the critical value and decision rule. (5p) d) Calculate the test statistic and draw conclusion. (5p) Most of the students in the group claim that the taste of White Lightning Cola is identical to the taste of Coca-Cola. Jane, one of the students, claims that she can tell the difference. The other students pour eight glasses of soda in unmarked glasses, four Coca-Cola and four White Lightning Cola, while Jane is not present. Jane is then told to guess which four glasses contain White Lightning Cola. She picks out all four correctly. e) Find the probability that someone guesses four out of four correctly, if they cannot tell the difference at all and they just guess. (5p)