Market researchers would like to know if consumers can taste the difference between a product made with low calorie oil and the same product made with regular oil. A random sample of 400 people are blindfolded and given both products to taste. Overall, 230 people correctly guess which is the low-calorie product.Is there evidence of a difference in taste of the two products?Answer Sample percentage of correct guesses is 1.5 standard errors above 50%, so there is no evidence of a difference in taste. Sample percentage of correct guesses is 2.0 standard errors above 50%, so there is no evidence of a difference in taste. Sample percentage of correct guesses is 3.0 standard errors above 50%, so there is evidence of a difference in taste.
Hi,Thank you for using JustAnswer.This question is phrased in a somewhat unusual manner, so I'll include my reasoning for the answer here as well.It would seem that the hypothesized value for the proportion of people who can correctly guess which is the low-calorie product is 0.50. This would indicate that customers can't tell the difference, since there is a 50-50 chance of guessing correctly. The test here is whether the proportion would be significantly different from 50%.The mean or expected value would then be µ = np = (400)(0.50) = 200The standard error would be σ = √npq = √(400)(0.5)(0.5) = 10Since the actual difference between the observed value (230) and the expected value (200) is 30, and this difference is 3 times the value of the standard error, the answer would be C. Sample percentage of correct guesses is 3.0 standard errors above 50%, so there is evidence of a difference in taste.Thanks,Ryan
Experience: B.S. in Civil Engineering