PSY 555 Homework 7
Answers
4.3. See HW#6 answers
4.4. See HW#6 answers
4.5. See HW#6 answers
4.7. Was
the son of the member of the Board of Trustees fairly admitted to graduate
school?
Z=_{}
Z=_{}→.0007
The
probability that a student drawn at random from those properly admitted would
have a GRE score as low as 490 is .0007.
Thus, there is reason to suspect that the fact that his mother was a
member of the Board of Trustees played a role in his admission.
4.9. The
distribution would drop away smoothly to the right for the same reason that it
always does—there are few high-scoring people.
It would drop away steeply to the left because fewer of the borderline
students would be admitted (no matter how high the borderline is set).
4.13.The alternative hypothesis is that this
student was sampled from a population of students whose mean is not equal to
650.
4.14.Sampling error is variability in a
statistic from sample to sample that is due to chance—i.e., due to which
observations happened to be included in the sample.
4.15.The word “distribution” refers to a set
of values obtained for any set of observations.
The phrase “sampling distribution” is reserved for the distribution of
outcomes (either theoretical or empirical) of a sample statistic.
4.17(a).
Research hypothesis: Children who
attend kindergarten adjust to 1^{st} grade faster than those who do not
attend. Null hypothesis: 1^{st}
grade adjustment rates are equal for children who did and did not attend kindergarten.
4.17(b).
Research hypothesis: Sex
education in junior high decreases the rate of pregnancies among unmarried
mothers in high school. Null
hypothesis: The rate of pregnancies
among unmarried mothers in high school is the same regardless of the presence
of absence of sex education in junior high school.
4.20.In section 4.11, we were running a
one-tailed test so we compared the obtained probability (.017) to .05 (placing
the full 5% in the single tail) and rejected H_{0}. If we were using a two-tailed test, we would
compare the obtained probability (still .017) to .025 (placing 5%/2=2.5% in
each tail) and would still reject H_{0}. In this case, therefore, the results would
have been the same in either case.
1.
α
and β are inversely related. So, if
α gets larger, then β decreases.
Power is defined as 1- β, so the smaller β is, the more power
you will have. Thus, switching from an
α=.01 to α=.05 will increase power.
However, the larger α also means that there will be greater
probability of a Type I error.
2. μ=100
σ=15
X |
_{} |
85 |
62.5681 |
90 |
8.4681 |
99 |
37.0881 |
103 |
101.8081 |
100 |
50.2681 |
86 |
47.7481 |
97 |
16.7281 |
83 |
98.2081 |
101 |
65.4481 |
91 |
3.6481 |
87 |
34.9281 |
_{} _{}526.9091
N=11 _{} s=_{}
SE=_{}
Z=_{}
The
IQ scores of cocaine addicts do not differ significantly from the IQ scores of
the general population.
3. There
is really no right or wrong answer to this question so long as you have
adequate justification for your decision, as a case can be made for using
either value. For instance, a person may
argue that a Type I error is better in this case, if an error must be made,
than is a Type II error (i.e., better to perhaps inaccurately conclude that a
drug helps treat AIDS patients, when in fact it does not, than to conclude the
drug has no beneficial effect when in fact it does). Another person, however, could argue that is
would be worse to make a Type I error because it could waste time researching
and using a drug on AIDS patients that has no benefit, when that time and
effort could be more appropriately devoted to finding a drug that actually
treats AIDS (i.e., the delay caused by inaccurately believing the drug to be
effective against AIDs, when it is not, could cost a lot of AIDs patients their
lives…since their treatment is entirely ineffective.