PSY 555 Homework 7

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 1st grade faster than those who do not attend.  Null hypothesis: 1st 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 H0.  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 H0.  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.