Question

22.39 Order in choice. Does the order in which wine is pre 4st p sented make a dlifference! Several choices of wine are pre- sented one at a time and in sequence, and the subject is then asked to choose the preferred wine at the end ot the sequence. In this study, subjects were asked to taste two wine samples in sequence. Both samples given to a subject were the same wine, although subjects were expecting to taste two different samples of a particular variety. Of the 32 subjects in the study, 22 selected the wine presented irst, when presented with two identical wine samples.29 (a) Do the data give good reason to conclude that the subjects are not equally likely to choose either of the two positions when presented with two identi- cal wine samples in sequence?

Answer 1

Let proportion be p for the people prefering first wine. It should be 0.5 if there is no sequential preference We want to test whether hypothesis Ho:p=0.5 H, : p+ 0.5 This is two tailed tes (Null Hypothesis) (Alternate Hypothesis, also called Hi) r 22 Sample proportion, p=-=-= 0.6875, n = 32 and claimed proportion, P-0.5 Significance level, α 0.05 n 32 now, calculating statistics Standard Deviation of p, ơp 0.5 x (1-0.5) 32 0.0884 p-0.5 (0.6875)-0.5 0.0884 Test statistic, Zobserved 2.121322.121 Since this is two tailed test, p-value = 2 × P(Z <-1801) = 2 × P(Z < -2.121) = 0.0338 Note that exact p-value is: 0.0338948535 Rejection Criteria: Reject Ho if p-value < α Decision : Since p-value < α, we reject the null hypothesis. Hence at 5% significance level, we have sufficient evidence to conclude that p is not equal to 0.5 Alternately, we can use Ctritical value approach, Critical value zc-in/2-20.05/2-20.025-1 calc Rejection Criteria: Reject Ho if zo is not in between (-1.960,1.960) Rejection region has been shaded 0.025 0.025 1.960 1.96 Decision : Since | > zc , we reject the null hypothesis. Hence at 5% significance level, we have sufficient evidence to conclude that p is not equal to 0.5, i..e, people do have a sequential preference Thank You