2. (5 marks) a) A wine aficionado makes the claim that he can tel the difference

Question

2. (5 marks) a) A wine aficionado makes the claim that he can tel the difference between red anod white wine while blindfolded. He tastes 50 wines of differing colour (he doesn't drink the wines, merely tastes them, otherwise his performance is going to get worse!) and he correctly identifies the colour of 31 wines. Perform a hypothesis test at the 0.01 significance level where the null hypothesis is that the taster is merely guessing and the alternative hypothesis that he performs better than if he were guessing. What is the conclusion? Hint: What is the test statistic in this case, how can this be approximated? b) Suppose that the probability that the taster correctly identifies the colour of wines is p-0.6. what is the power of the hypothesis test from part (a)? c) The aficionado's wife also tastes the same 50 wines, she correctly identifies the colour of 29 wines. Perform a hypothesis test at the 0.01 significance level, where the null hypothesis is that they have the same probability of selecting the correct colour of the wines, and the alternative is that the probabilities differ. What is the conclusion? Be careful to cdearly state any assumptions made)

Explanation / Answer

a)

Ho: p = 0.5

Ha: p > 0.5

X = 31 , n = 50

Z = (p^ - p)/sqrt(pq/n)

= 1.7

p-value = P(Z > 1.7) = 0.045

since p-value > 0.01

we fail to reject the null hypothesis

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