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Kenneth Ryan J.
High School Graduate, 4.35 GPA, Seal of Biliteracy
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Psychology
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Question:

What are the 3 portions of one's personality believed in by Freud?

Kenneth Ryan J.
Answer:

The id is the first portion, believed to be one's desire for basic needs. The ego comes next and is defined as dealing with reality. Finally, the superego is supposed to represent morality in humans. This concept has long been considered to be false.

Calculus
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Question:

lim(x->0) sin(x)/x

Kenneth Ryan J.
Answer:

While seemingly impossible at first, this derivative passes l'hopitals test. To find the asnwer, simply take the derivative of both the top and bottom of the equation, but separately. Thus, the problem is turned into (d/dx(sinx))/(d/dx(x)). This results in cos(x)/1, which approaches 1 as x approaches 0.

Statistics
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Question:

A running shoe company claims that at least 64% of its customers enjoy running. A simple random sample of 493 people who have purchased shoes from this company in the past 6 months asked the following question: do you enjoy running? 300 out of the 493 people answer yes to this question. Using a significance level of .05, conduct a hypothesis test to see if the company's claim is true.

Kenneth Ryan J.
Answer:

Using the formula sqrt(p(1-p)/N)= the standard deviation, where p is the hypothesized proportion and N is the population number, we get a standard deviation of 0.0216. Next, the test statistic can be found using the formula z=(P-p/Sx), where P is the found proportion and Sx is the standard deviation. Doing this results in a test statistic of 28.172. On a normal z scale, this would result in a p value of essentially 0. With a p-value as small as this, we can reasonable conclue that results as extreme as shown would occur 0 times due to sampling variability. When compared to a significance level of 0.05, this proportion fails this hypothesis test. We do not have enough evidence to conclude that the shoe campany's claim is true.

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