Diners at a restaurant were informed on entering that they would be receiving a
ID: 3233230 • Letter: D
Question
Diners at a restaurant were informed on entering that they would be receiving a free glass of wine, which they were told was Cabernet Sauvignon. However, it was not. It was a cheap wine sold for $2 a bottle, popularly know as Two Buck Chuck. Half of the diners were told that the wine was from a new California winery. The other half of diners were informed that the wine they would receive was from a new North Dakota winery. (There are no wineries in ND and even if there were the wine produced would not be considered excellent.) The goal of the experiment was to determine whether the perceived quality of the wine affected their dining experience. The amount of food consumed (measured as a percentage of the amount originally served that was consumed by the diners,so that 100 represents a diner who cleaned his or her plate) and the amount of time spent in the restaurant were recorded. (Xr13-39) You can assume equal variances.
PART 1: Is there enough statistical evidence to infer that the diners who believe they are drinking a fine wine (California wine) eat more than diners who believe they are drinking an inferior wine?
PART 2: Is there enough statistical evidence to infer that the diners who believe they are drinking a fine wine (California wine) spend more time in the restaurant than diners who believe they are drinking an inferior wine?
Cal Wine Consumed Cal Wine Time SD Wine Consumed SD Wine Time 100 58 100 50 100 76 90 74 100 63 85 72 90 60 90 61 100 58 100 51 95 72 100 69 100 75 100 56 100 58 100 53 100 62 80 62 100 73 95 68 100 41 100 44 100 67 100 43 90 51 85 59 100 72 95 58 100 49 100 51 100 64 100 64 100 75 85 64 90 81 85 46 80 62 100 46 100 69 100 54 100 67 100 70 100 63 100 59 100 56 100 52 100 64 80 50Explanation / Answer
Test and CI for Two Variances: Cal Wine Consumed, SD Wine Consumed
Method
Null hypothesis (Cal Wine Consumed) / (SD Wine Consumed) = 1
Alternative hypothesis (Cal Wine Consumed) / (SD Wine Consumed) 1
Significance level = 0.05
F method was used. This method is accurate for normal data only.
Statistics
95% CI for
Variable N StDev Variance StDevs
Cal Wine Consumed 24 5.103 26.042 (3.966, 7.158)
SD Wine Consumed 24 7.360 54.167 (5.720, 10.324)
Ratio of standard deviations = 0.693
Ratio of variances = 0.481
95% Confidence Intervals
CI for
CI for StDev Variance
Method Ratio Ratio
F (0.456, 1.054) (0.208, 1.111)
Tests
Test
Method DF1 DF2 Statistic P-Value
F 23 23 0.48 0.086
P-value -0.086 > 0.05 we do not reject null hypothesis. it can be concluded that, there is no enough evidence to infer that the population vatiances are different.
Paer 2. We use here two sample t test:
Two-sample T for Cal Wine Consumed vs SD Wine Consumed
N Mean StDev SE Mean
Cal Wine Consumed 24 97.71 5.10 1.0
SD Wine Consumed 24 94.58 7.36 1.5
Difference = (Cal Wine Consumed) - (SD Wine Consumed)
Estimate for difference: 3.13
95% lower bound for difference: 0.05
T-Test of difference = 0 (vs >): T-Value = 1.71 P-Value = 0.048 DF = 40
P-value < 0.05 we reject null hypothesis. So there is an evidence to inter that the diners who believe they are drinking a fine (California wine ) eat more than diners who belive they are drinking an inferior wine.