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3. The manufacturer of Coke claims that brand A soda is preferred twice as much as both Pepsi and RC Cola soda in a taste-test. A student wants to know if this claim is true for all students at her school and uses a random sample of 160 students for a double-blind taste-test. Students were asked to state their preference for either brand Coke, Pepsi, or RC Cola. Here are the results. Observed number of choices for each soda brand --IEM Observed number choosing 46 brand (a) The student wants to carry out a test to see if the distribution of soda preference among the three brands for all students at her school is different from the distribution claimed by the manufacturer of Coke. State the null and alternative hypotheses for this test. (b) Find the expected counts for each brand under the assumption that the null hypothesis is true. Expected number of choices for each soda brand. --IEE Observed number choosing --- brand (c) Discuss whether the conditions for this test have been met. (d) Find the value of the test statistic and the P-value of the test, and make the appropriate conclusion using a = 0.05. (e) Based on your answer to (d), which error may you have made, Type I or Type II? Describe that error in the context of the