A producer of chocolate candy bars has developed an improved recipe for one of their most popular brands. They are conducting taste tests using randomly selected mall shoppers. One hundred shoppers were given the original recipe bar to taste and to rate it on a scale of 1 to 10. Another hundred shoppers were given the new recipe candy bar to taste and to rate it on a scale of 1 to 10. The results are in the table below for statistical analysis. All of these analyses are run with a 95% level of confidence.
Use this information to answer the following questions.
(a) Find the difference between these sample means.
(b) Find the variance of the original recipe sample.
(c) Find the variance of the new recipe sample.
(d) Which test should be run to determine if there is evidence of a difference in consumer preferences between the two recipes?
(i) A pooled variance t-test for the difference between two means.
(ii) A t-test for the difference between two means assuming unequal variances.
(iii) A paired t-test.