A Business School Has Found That Over the Years, Out

question 14

Essay

A business school has found that over the years, out of all the students who are offered
admission, the proportion who accept is 0.70. After a new director of admissions is
hired, the university wants to check if the proportion of students accepting has changed
significantly. Suppose they offer admission to 1200 students and 888 accept. Is this
evidence of a change from the status quo?
A. Write the null and alternative hypotheses.
b. Let's perform a one sample z-test for proportions: What is the value of the test statistic?
c. What is the associated P-value?
d. State your conclusion using α = 0.05.

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Definitions:

Symbolic Functioning

The ability to use symbols, signs, or objects to represent something else, a milestone in cognitive development allowing for complex thought.

Concrete Operations

A stage in Piaget's theory of cognitive development, typically from ages 7 to 11, when children gain the ability to think logically about concrete events.

Sensorimotor Period

The first of Jean Piaget's four stages of cognitive development, ranging from birth to about 2 years old, where infants learn about the environment through sensory experiences and motor activities.

Egocentrism

The cognitive inability to differentiate between one's own perspective and that of others, often seen in early childhood.