The 49 students in a class at the University of Georgia made blinded evaluations
ID: 3052751 • Letter: T
Question
The 49 students in a class at the University of Georgia made blinded evaluations of pairs of cola drinks. For the 49 comparisons of Coke and Pepsi, Coke was preferred 29 times. In the population that this sample represents, is this strong evidence that a majority prefers one of the two drinks? Refer to the following output. (These are all multiple choice questions: 1, 2, 3, or 4?...or 5?)
(a) Explain how to get the test statistic value that the output reports.
(1) Subtract 0.5 from p? and divide by n.
(2) Subtract p? from 0.5 and divide by the standard error.
(3) Subtract 0.5 from p? and divide by the standard error.
(4) Subtract 0.5 from p? and divide by the square root of n.
(b) Explain how to get the p-value.
(1) Find the probability above 1.286 and below -1.286 on the standard normal distribution.
(2) Find the probability below -1.286 on the standard normal distribution.
(3) Find the probability above 1.286 on a uniform distribution from 0 to 2.
(4) Find the probability above 1.286 on the standard normal distribution.
(c) The P-value in this question is 0.199. Which of the following is true?
(1) If UGA students truly DO have a preference between Coke and Pepsi, about 29% of the possible samples would have proportions that would fall at least this far from 0.50.
(2) If UGA students truly have NO preference between Coke and Pepsi, about 19.9% of the possible samples would have proportions that would fall at least this far from 0.50.
(3) If UGA students truly DO have a preference between Coke and Pepsi, about 19.9% of the possible samples would have proportions that would fall at least this far from 0.50.
(4) If UGA students truly have NO preference between Coke and Pepsi, about 29% of the possible samples would have proportions that would fall at least this far from 0.50.
(d) Based on the result in (b), does it make sense to "accept Ho"? Explain.
(1) Yes, the P-value is greater than 0.05.
(2) Yes, the P-value is less than 0.05.
(3) No, the P-value is greater than 0.05.
(4) No, the P-value is less than 0.05.
(5) No, we never accept a null hypothesis. We can only fail to reject it.
(e) What does the 95% confidence interval tell you that a hypothesis test does not?
(1) the exact value of p
(2) the range of plausible values of p
(3) that p has to be below the upper bound
(4) that p has to be above the lower bound
Test of p = 0.50 vs. p ? 0.50 X N p? 95.0% CI Z-Stat P-Value 29 49 0.5918 (0.454, 0.729) 1.286 0.199Explanation / Answer
a)(2) Subtract phat from 0.5 and divide by the standard error.
b) (4) Find the probability above 1.286 on the standard normal distribution.
c) (2) If UGA students truly have NO preference between Coke and Pepsi, about 19.9% of the possible samples would have proportions that would fall at least this far from 0.50.
d)
(5) No, we never accept a null hypothesis. We can only fail to reject it.
e)
(2) the range of plausible values of p
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