Question

An alternative “healthy” recipe is being tested as a substitute for a favorite menu item at a fast-food restaurant. In a masked taste test 10 participants were asked to rate each of the standard menu item and the “healthy” alternative on a scale of 1 to 10. The 90% confidence interval estimate of the mean difference in the ratings was (–0.9, 1.3). Suppose the restaurant management specify that a mean difference in ratings of less than 1 point is not important. Based on this standard, can we conclude that the mean ratings for the standard menu item and the healthy alternative are equivalent with significance level 0.05?

a) yes, because 0 is within the confidence interval.

b) yes, because 1 point is within the confidence interval

c) no, because the confidence level and the significance level don't match.

d) no, because the confidence interval is not within (–1, 1).

Answer 1

Sol:

Ho:

mean ratings for the standard menu item and the healthy alternative are equivalent

Ha:

alpha=0.10

The 90% confidence interval estimate of the mean difference in the ratings was (–0.9, 1.3)

since 90% confidence interval contains zero

Do not reject Ho

Accept Ho

mean ratings for the standard menu item and the healthy alternative are equivalent

a) yes, because 0 is within the confidence interval.