Question

In a larger Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose of fell the next day and report their proportion of "successes". As a lesson, the professor has selected pages of the Journal for which exactly half the publically traded stocks went up and half went down. The professor then makes a histogram of the reported proportions.

a) What shape would you expect this histogram to be? Why?
b) Where do you expect the histogram to be centered?
c) How much variability would you expect among these proportions?
d )Explain why a normal model should not be used here.

Answer 1

A.- Normal

B.- Centered at the true proportion (see imagen)

C.- SE(p)=0.125

D.- There’s no way the histogram could ever look like a Normal model with only two possible values for the variable

Explanation:

A.- Normal

Based on the Central Limit Theorem (CLT) that states:

"The mean of a random sample has a sampling distribution whose shape can be approximated by a Normal model". The larger the sample, the better the approximation will be.

B.- See attached graph

C.- SE(p)=
`√(pq/n)=\sqrt[n]{(0.5)(0.5)/16}=0.125`

D.- Success/Failure Condition:

The Success/Failure condition says that the sample size must be big enough so that both the number of “successes,” np and the number of “failures,” nq, are expected to be at least 10.

np=(16)(0.125)=2 not enough