Case Study # 1

Last year Ben&Tom decided to enter the yogurt market, and it began cautiously by producing, distributing, and marketing a single flavor - a blueberry-flavored yogurt that it calls Mirtillo. The company's initial venture into the yogurt market has been very successful; sales of Mirtillo are higher than expected,and consumers' ratings of the product have a mean of 85 and a standard deviation of 36 on a 100-pointscale for which100is the most favorable score andzerois the least favorable score. Past experience has also shown Ben&Tom Dairies that a consumer who rates one of its products with a score greater than80on this scale will consider purchasing the product, and a score of80or less indicates the consumer will not consider purchasing the product.

Emboldened by the success and popularity of its blueberry-flavored yogurt, Ben&Tom

Dairies management is now considering the introduction of a second flavor. Ben&Tom's marketing department is pressing to extend the product line through the introduction of a strawberry-flavored yogurt that would be called Fragola, but senior managers are concerned about whether or not Fragola will increase Ben&Tom's market share by appealing to potential customers who do not like Mirtillo. That is, the goal in offering the new product is to increase Ben&Tom's market share rather than cannibalize existing sales of Mirtillo. The marketing department has proposed giving tastes of both Mirtillo and Fragola to a simple random sample of100customers and asking each of them to rate the two flavors of yogurt on the 100-point scale. If the mean score given to Mirtillo by this sample of consumers is 80 or less, Ben&Tom's senior management believes the sample can be used to assess whether Fragola will appeal to potential customers who do not like Mirtillo.

Managerial Report

Rubric:Correct &Clear Explanation90- 100%,Correct & Bad Explanation(not clear....)51% - 85%,Correct no Explanation50%,Incorrect & Bad(incorrect, not clear....)Explanation10% - 40%,Incorrect and no Explanation0%

Prepare a managerial report that addresses the following issues.

1. Calculate the probability the mean score of Mirtillo given by the simple random sample of Ben&Tom Dairies customers will be80or less.(25pts)
2. If the Marketing Department increases the sample size to256, what is the probability the mean score of Mirtillo given by the simple random sample of Ben&Tom Dairies customers will be80or less?(25pts)
3. Explain to Ben&Tom Dairies senior management why the probability that the mean score of Mirtillo for a random sample of Ben&Tom Dairies customers will be80or less is different for samples of100and256Ben&Tom Dairies customers.(25pts)
4. Develop a95%confidence interval estimate of the population mean consumers' rating for the Mirtillo product. The sample size is100, the sample mean is 80 and the standard deviation of thepopulationis 36 (must use the z table) -(25pts)