Question

A company, United Foods, decided to enter the yogurt market by introducing a single flavor yogurt, a pumpkin flavor called PumpGurt. In last one year, company found that this flavor is very successful among consumers with average consumer rating score of 85 (with rating score from 0 to 100) and a standard deviation of 25. The United Foods believes that any consumer who rates its products 80 or higher is likely to purchase it and those who give a score lower than 80 will not consider buying it. With success of PumpGurt, company wants to introduce a new cherry flavor, CherryGurt. The company is hoping to lure those customers who do not like PumpGurt and increase its overall market share in yogurt market. The company does not want to cannibalize existing sales of PumpGurt by introducing CherryGurt.

To test new flavor, CherryGurt, marketing department of United Foods intends to do a taste test of both PumpGurt and CherryGurt using a random sample of 50 people and asking them to rate both using score from 0 to 100. If the mean score given by this sample for PumpGurt is less than 80, this sample can be used by the company whether CherryGurt will appeal to potential customers who do not like PumpGurt.

a. Compute the probability that this sample of 50 people can be used by the company to test whether CherryGurt will appeal to potential customers who do not like PumpGurt. Based on your results, what is your recommendation to the company regarding use of this sample of 50 people to test appeal of CherryGurt to potential customers?

b. If the marketing department increases the sample size to 150, compute the probability that this sample of 150 people can be used by the company to test whether CherryGurt will appeal to potential customers who do not like PumpGurt.

c. Explain to senior management of United Foods why the probability in part a and part b are different for two sample sizes i.

Answer 1

ANSWER::

Z= (Xbar - mean)/(Sigma/sqrt(n)) = (Xbar - 85)/(25/sqrt(n)))

a)

n = 50

P(Xbar < 80)

= 0.0786

b)

n = 150

P(Xbar < 80)

= 0.0072

c)

probabilities are different due to the sample size difference

when sample size increases

margin of error decreases

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