# The case information stated that 66% of teenagers purchase

Question

McCain Frozen Pizza Targets Teens

*left out unnecessary case description* Within the first six months of the new advertising campaign, McCain was able to double its sales goal of a 15% increase for the Crescendo Rising Crust Pizza to a 34% year-over-year increase in ex-factory sales.

In the research process for McCain Foods Limited, many different numerical questions were raised regarding advertising techniques and purchase patterns amongteenagers. In each of these areas, statistics, in particular hypothesis testing, plays a central role. Using the case information and the concepts of hypothesis testing, discuss the following:

a) The case information stated that 66% of teenagers purchase products that reflect their style and image as being hip and trendy. How would you test the appropriateness and validity of that percentage? In a test where 900 teens are randomly selected across Canada, 625 state that they purchase products that reflect their style/image as being hip and trendy. Test the claim made in the case regarding the purchase of products by teenagers reflecting their style and image. Use a significance level of 5% to help you reach a suitable statistical decision. What would be the probability of discrediting the claimed percentage (of 66%) if in fact it were true?

b) Historically, it has been verified that 72% of all teens that ate frozen pizza were girls. Due to apparent changes in gender tastes, it is believed that more teen boys are now eating frozen pizzas. From a random sample of 653 teens that eat frozen pizza, 513 are girls. Does this sample result provide sufficient evidence to conclude that a higher proportion of teenage girls than before eat frozen pizza?

c) What is the proportion of the teenage population that watches advertisements on television? It has been claimed by a reputable source that, historically, this proportion has been in the neighbourhood of 0.87. McCain researchers want to test whether this figure is true. A random sample of 612 teens is selected. The results of the hypothesis-testing procedure are shown below. Analyze the results shown in the output below, and discuss and explain its contents, as well as any subsequent implications this sample study might have on the behavioural spending patterns of the teenage population as a result of television advertising viewings. To perform this analysis, use alpha = 0.05.

Test of p = 0.87 versus. p does not = 0.87

x = 490

n = 612

sample p = 0.800654

95% CI (0.769002, 0.832306)

Exact p value 0.0035

2. The statistical mean can be used to measure various aspects of the teen market, including amount spent, age of teenage consumers, etc. Use techniques presented in this chapter to analyze each of the following and discuss the results in the context of the case information.a) What is the average age of the teenage consumer of the Crescendo Rising Crust Pizza? Suppose that initial beliefs indicate that the mean age is 15. Is this figure really correct? To test whether it is, a researcher randomly contacts 30 teenage consumers of Crescendo Rising Crust Pizza, with results shown in the following output. Discuss the output in terms of a hypothesis test to determine whether the mean age is actually 15. Let alpha = 0.01. Assume that the distribution of the ages of all teenage consumers is mapped as a normal distribution.Mean = 16.92Variance = 30.2963Observations = 30df = 29t Stat = 1.91P (T>=t) one-tail = 0.0348t Critical one-tail = 2.46P (T>=t) two-tail = 0.0696t Critical two-tail = 2.76

b) What is the average number of frozen pizzas that teens consume per year? Suppose it is hypothesized that the figure is 37 pizzas per year. A research who is knowledgeable of the teenage market claims that this figure is excessive and is prepared to prove it. He randomly selects 20 teens, has them keep a log of foods they eat for one year, and obtains the following figures. Analyze the data using techniques from this chapter and an alpha of 0.05. Assume that the number of frozen pizzas per end-user is a normally distributed variable in the population

numbers given:10, 11, 13, 14, 16, 17, 18, 23, 29, 29, 33, 35, 36, 37, 38, 39, 43, 45, 52, 58

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