Discuss the following:
Q. The 65 students in a class at the University of Soda were given blinded evaluations of pairs of cola drinks. For the 65 comparisons of Coke and Pepsi making up the sample results, Pepsi was preferred 29 times.
a. Is the above information sufficient for you to be completely certain that more than 50% of all students at that university prefer Coke over Pepsi? Why or why not?
b. In establishing a statistical hypothesis testing of this situation, give the required null and alternative hypotheses for such a test.
c. Based on your answer in part b, should you use a right-tailed, a left-tailed, or a two-tailed test? Explain how one determines which of the three possibilities is to be used.
d. Describe the possible Type I error for this situation--make sure to state the error in terms of the student's preference of Coke over Pepsi.
e. Describe the Type II error possible in this situation--make sure to state the error in terms of the student's preference of Coke over Pepsi.
f. Determine the appropriate critical value(s) for this situation given a 0.05 significance level.
g. Determine/calculate the value of the sample test statistic.
h. Detemine the P-value in this test.
i. Based upon your work above, is there statistically sufficient evidence to support that a majority, more than 50%, of students prefer Coke over Pepsi?? Briefly explain your reasoning.