The Makers of Compute-All Know That in the Past, 40

question 39

Essay

The makers of Compute-All know that in the past, 40% of their sales were from people under 30 years old, 45% of their sales were from people who are between 30 and 50 years old, and 15% of their sales were from people who are over 50 years old. A sample of 300 customers was taken to see if the market shares had changed. In the sample, 100 of the people were under 30 years old, 150 people were between 30 and 50 years old, and 50 people were over 50 years old.
a.State the null and alternative hypotheses to be tested.
b.Compute the test statistic.
c.The null hypothesis is to be tested at the 1% level of significance. Determine the critical value from the table.
d.What do you conclude?

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Definitions:

Fallacy of Composition

Erroneous view that what is true for the individual (or the part) will also be true for the group (or the whole).

Association

An organization or group of individuals who voluntarily come together to achieve common goals, often representing a profession, industry, or interest.

Causation

The relationship between cause and effect where one event or action directly leads to another event or action as a result.

Macroeconomics

The branch of economics dealing with the structure, performance, behavior, and decision-making of an economy as a whole, rather than individual markets.