**1.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 and image as being hip and trendy. The test that 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?

1.b.

Historically, it has been verified that 72% of all teens who 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 who 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?

**Case: McCain Frozen Pizza Targets Teens**

**About the Company**

McCAIN Foods Limited is an international leader in the frozen food industry, employing 20,000 people and operating 50 production facilities on six continents. A privately owned company headquartered in Toronto, Canada. McCAIN is the world’s largest manufacturer of frozen potato specialties and also produces other food products, including pizza, appetizers, oven meals, juice and desserts. The company’s products can be found in thousands of restaurants and supermarket freezers in more than 160 countries around the world.

McCain's Product Line

Fruits and Veggies

**By: Group 6**

Cabalona, Christian

Delos Reyes, Vanessa

Graza, Maria Louise Joy

Cabalona, Christian

Delos Reyes, Vanessa

Graza, Maria Louise Joy

Regular Vegetables

Potatoes

Vegetable Mixes

Meals, Pizza and Snacks

here, p = 0.66 , n = 900

= 625 / 900 = 0.694

thus, z = 0.218

Since the z value calculated is between -1.96 and +1.96 the null hypothesis is not rejected. There is no sufficient evidence to say that purchase of products by teenagers reflecting their style and image is different from 66%

HYPOTHESIZE

Let p be the proportion teen girls eating pizza.

The null hypothesis is that 72% of all teens who ate frozen pizza were girls.

TEST

The statistical test to be used is

P = 0.72, N=653,

Z = -0.2846

ACTION

Since the Z value is with in (-1.645,1.645) , the null hypothesis is not rejected. Thus not enough evidence to claim that percentage is different from 0.72.

1.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 behavioral spending patterns of the teenage population as a result of television advertising viewings. To perform this analysis, use

Test and CI for One Proportion

Sample x N Sample p 95%CI Exact p-value

1 490 612 0.800654 (0.769002, 0.832306) 0.0035

Let p be the proportion of teenage which watches advertisements

490 /612 is the sample proportion which is 0.8

The p value from the output is 0.0035 which is less than 0.05. Thus there enough evidence to reject the null hypothesis. The 95% CI means that out of 100 samples , 95 samples would have the proportion in the range (0.769002, 0.832306)

2.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 α be 0.01. Assume that the distribution of the ages of all teenage consumers is mapped as a normal distribution.

HYPOTHESIZE

The null hypothesis is that the mean age still equals 15. Did not specify whether he believes that the age is older or younger than 15 so a

two-tailed test

is appropriate.

TEST

The statistical test to be used is

The value of alpha is 0.01

Because n = 30, the degrees of freedom for this test are 29 (30-1).

The gathered data are shown

The observed t value as given is 1.91.

ACTION

The observed t value of 1.91 is less than the t table value (Excel) of 2.76 for two-tail test. Also, when using the p-value and critical value method to test the hypothesis (if the mean age is not equal to 15), we get the two-tailed p–value in this case. Since the p-value is greater than α 0.01(0.0696), the hypothesis is not rejected or there is not enough evidence for rejecting the hypothesis

Let p be the proportion of teenagers who purchase products that reflect their style and image as being hip and trendy

HYPOTHESIZE

TEST

The statistical test to be used is

ACTION

2.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 researcher 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.

HYPOTHESIZE

Determine if the average number of frozen pizzas that teens consume per year is really 37 pizzas per year.

TEST

The statistical test to be used is

The value of alpha is 0.05

n = 20, df = 19 (20-1). This test is one-tailed, and the critical table t value is

The gathered data are shown.

The sample mean is 29.8 and the sample standard deviation is 199.53. The observed t value is

ACTION

In using the Critical value method, since the p-value is less than the alpha 0.5 or at 5% level of significance, the null hypothesis is rejected. Teens eat significantly less than 37 pizzas per year.

Mc Cain Frozen Pizza can further do more research in this new finding where teens eat significantly less pizza than what used to be believed in. It could mean that the number has decreased over time or that the figure was indeed excessive and not representative of teens’ eating preferences. This can also aid the company so they can look into strengthening their product development and marketing strategies to help them promote their pizzas and drive higher consumption from their target market.

The test does not result in enough evidence to conclude that the mean (average) age is not anymore 15. McCain Frozen Pizza can continue to direct their marketing efforts to this age group to cater their needs and listen to their wants.