Suppose you were hired to determine if college students could tell the difference in tastebetween Sprite and Sierra Mist. You conducted a study by randomly sampling 90 students from a largelecture on the Oregon State University campus. Each student was individually brought to a tasting roomwhere three cups with lids were placed in front of them. Two of the cups contained one of the brands ofsoda (say Sprite) and the other cup contained the other brand of soda (Sierra Mist). Students did not know which brand was in which cup. Using a straw that was placed through the lid of each cup, each student was to taste the soda in each cup and report to you which cup they thought contained the different brand.
Suppose 52 of the 90 students were able to correctly identify the cup that contained the different brand ofsoda. Is that evidence that college students could tell the difference in taste between Sprite and Sierra Mist?
a. What is the random variable in this problem? Does the random variable have a binomial distribution?Explain.
b. What does p represent in the context of this study?
c. Calculate the sample proportion, ˆp , of people in the study who could identify the cup that contained the different brand of soda. Show work.
i] State the null and alternative hypotheses in statistical notation AND in words!!
ii] Assume that the observations are independent of each other. Which hypothesis test is the
appropriate one to use in this situation? Why?
.iii] Perform the appropriate hypothesis test. Report the test-statistic and p-value.
iv] Based on the p-value, answer the question of interest in a complete sentence in the context of the
problem.
f. calculate the standard deviation for the one-sample z-methods
i] By hand, calculate the standard deviation of the sample proportion ( ˆp σ ) used to perform the
hypothesis test. Show work.
ii] By hand, calculate the standard deviation of the sample proportion used in the calculation of theconfidence interval. Show work.
iii] Why does the formula for the standard error when doing a confidence interval use the sample proportion instead of the hypothesized value of the population proportion?