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Suppose That We Are Studying the Purchasing Behavior of Individuals

question 21

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Suppose that we are studying the purchasing behavior of individuals buying breakfast oatmeal. We hypothesize that half the cereal purchases will be the big name brand, "Seabiscuit Oats" and that the remaining purchases will be divided equally between two local brands, "Secretariat Oats" and "Whirlaway Oats."
a) Define appropriate statistical variables, and use them to state the null and alternative hypothesis that would be used to decide if there was convincing evidence against the hypothesized distribution of purchases across the three brands.
b) Suppose that each individual in a random sample of 200 purchasers provides information about his or her choice of brand. For each category, what are the expected values?
c) How many degrees of freedom are associated with the chi-squared goodness-of-fit statistic?
d) Suppose that χ2 = 6.10. What can be said about the P-value for this hypothesis test?

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Definitions:

Adolescents

Young people in the transition stage from childhood to adulthood, typically between the ages of 10 and 19.

Self-understanding

The awareness and comprehension of one's own personality, emotions, motivations, and capabilities.

Personal Fable

A cognitive distortion experienced by adolescents who believe themselves to be unique, invulnerable, and misunderstood.

Middle-aged Adults

Individuals typically between the ages of 40 and 60, experiencing the mid-stage of adulthood often marked by certain life transitions and health considerations.

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