PSY 555 Homework 10

Answers

Chapter 5: #17,18,27,28

5.17(a). Mean
ADDSC score for boys=54.29, s=12.90 [calculated from the Data Set]

*z*=_{}

Since
a score of 50 is below the mean, and since we are looking for the probability
of a score greater than 50, we want to look in the tables of the normal
distribution in the column labeled, "larger portion."

*p*(larger
portion)=.6293

5.17(b). _{} (Notice that one
percentage refers to the proportion greater than 50, while the other
refers to the proportion greater than or equal to 50).

5.18. p(that person will drop out of school, given that he/she has
an ADDSC of at least 60)=_{}

5.27. Number
of subjects needed in Exercise 5.26's verbal learning experiment if each
subject can see only two of the four classes of words.

_{}

5.28. Chance
that a subject will press correctly on first trial when learning to press three
out of five buttons in a certain order:

_{}

There
are 60 possible orders to push 3 out of 5 buttons. The probability that the subject will choose
the correct order on the first trial=p(_{})=.017.

1. _{}

_{}

36-15=21

The
researcher has lost 21 pairings of pictures.

2. p=_{}

q=_{}

N=230

_{}

s=_{}

X=110

Z=_{}

There
is a .0089 probability of getting a score of 110 or greater.

3. The
central limit theorem essentially says that, regardless of the shape of the
population distribution, as *n*
increases, the sampling distribution of the means approaches normality and the
rate at which the sampling distribution approaches normality is a function of
how normally the actual population is distributed. Furthermore, the standard
deviation of the sampling distribution of the means (the standard error of the
means) equals _{} This
theorem is important because it allows us to use the normal distribution to
assess probability, regardless of the shape of the original distribution. We should be aware,
however, that the sampling distribution of s may not be normal, and therefore, the central limit theorem is
not a panacea for non-normal distributions.

4.
Estimates of parameters can be
based upon different amounts of information. The number of independent pieces
of information that go into the estimate of a parameter is called the degrees
of freedom (df). In general,
the degrees of freedom of an estimate is equal to the number of independent
scores that go into the estimate minus the number of parameters estimated as
intermediate steps in the estimation of the parameter itself. For example, if
the variance, σ^{2} , is to be estimated from a random sample of N
independent scores, then the degrees of freedom is equal to the number of
independent scores (N) minus the number of parameters estimated as intermediate
steps (one, μ is estimated by M) and is therefore equal to N-1.

5. The
*t*-distribution begins to approach the
*z*-distribution, or normality, as N
approaches infinity because as N increases, the noise in your sample estimates
(*s* as an estimate of
s) is reduced. The *t*-distribution is a special distribution
that is essentially the same as the *z*-distribution
with one important difference--the *t*-distribution,
unlike the *z*-distribution, accounts
for the sample error of the standard deviation.
So, as the sample error for the standard error is minimized (which
occurs the more N increases), the *t*-distribution
has less error to account for and approaches the *z*-distribution, which is normal.