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 companys 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 90 and a standard deviation of 36 on a 100-point scale for which 100 is the most favorable score and zero is 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 than 85 on this scale will consider purchasing the product, and a score of 85 or 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&Toms 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&Toms 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&Toms 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 of 100 customers 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 85 or less, Ben&Toms senior management believes the sample can be used to assess whether Fragola will appeal to potential customers who do not like Mirtillo.

Prepare a managerial report that addresses the following issues.

1. 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 be 85 or less is different for samples of 100 and 256 Ben&Tom Dairies customers.

2. Develop a 90% confidence interval estimate of the population mean consumers rating for the Mirtillo product. The sample size is 100, the sample mean is 85 and the standard deviation of the population is 36 (must use the z table). What the confidence interval lead you to conclude?