Name:__________________________________________
Midterm Exam #2 (200 points total)
Psychology 321
SECTION I (75 pts total = 15 questions x 5 pts): Write your answer in T (true) or F (false).
1. (25 pts.) Suppose you have a treatment which you suspect may alter performance on a certain task. You
compare the means of your control and experimental groups (say 40 subjects in each sample). Further,
suppose you use a simple independent means t test and your decision is a rejection of the null hypothesis
with t=3.30, df=78, and p < á=0.001. Given this result, determine whether each statement below is T
(true) or F (false):
__F___ (a) You have shown that there is a non-zero difference between the two population means.
__F___ (b) The probability of the null hypothesis being true given your decision is p.
__F___ (c) You can deduce the probability of the alternative hypothesis being true given the decision.
__F___ (d) You know the probability of making a type I error given the decision.
__F___ (e) You have a reliable experimental finding in the sense that if, hypothetically, the experiment
were repeated a great number of times, you would obtain a significant result on more than 99.9%
of occasions.
2. (50 pts.).
__F__ (a) Based on a sample, we have obtained a 95% confidence interval for ì as [1.4, 8.7]. This
means that the probability of this particular interval containing ì is 0.95.
__T__ (b) The favored hypothesis, H1, is held innocent unless proved guilty, while the other hypothesis,
H0, held guilty until no choice remains but to judge it innocent.
__F__ (c) A p-value of 0.23 means that given sample data, the probability of the null hypothesis
being true is 0.23.
__F__ (d) Suppose that the null hypothesis was retained with p = 0.18 > "= 0.05 in a test
whose power (1-")was 0.85. It is more than likely that a type II error was made in this case.
__F__ (e) The smaller the p-value, the more scientifically/practically significant result.
__T__ (f) For an experimental data, suppose that we have obtained p = 0.001, 1 - "= 0.99,
and d = 1.99. This result would be a real breakthrough, meaning a not only statistically
significant but also scientifically important result.
__F__ (g) Power of a test is determined by not only the alpha level but also the value of the sample mean
the null hypothesis.
__F__ (h) When the null hypothesis is rejected, one should look into power and effect size to determine
whether a type I error might be committed.
__F__ (i) Power of a test depends upon the sample mean as well as the sample size,.
__T__ (j) A larger p-value (e.g., p = 0.26) should not be interpreted as a result favoring the
null hypothesis, especially when power is low.
SECTION II (65 points total) (For full credit show your work and write down the formulas used.)
1. (65 pts.) In their reading study, Jandreau and Bever (1992) needed to understand something about their
subject's level of ability. They had available each subject's Verbal scale scores on the scholastic Aptitude
Test (VSAT). Their 25 subjects had a mean VSAT score of 470.0. Should that value lead Jandreau and
Bever to doubt that the population the subjects represent has :norm = 500 and Fnorm=100, which is the norm
for "average" subjects?
(a) (15 pts.) Test their hypothesis using a one-tailed z-test with " = 0.05, following the four-step
procedure, determine whether the p-value is smaller or greater than á, interpret the result, and provide the
scientific notation. (Assume F =100.)
Zcrit = -1.65 (since one-tailed)
Zobs = (470-500)/20 = -1.5
Reject Ho since Zobs = -1.5, p > " = 0.05.
(b) (10 pts.) Obtain a 95% confidence interval for the population mean of interest, and explain the interval
to someone who knows no statistics, especially what the "95% confidence" really means.
A 95% CI for : :
470 ±(1.96)(20) = (430.8, 509.2)
We are 95% confident in that the if analogous samples of size 25
have been drawn and corresponding confidence intervals have been
constructed, on average, 95% of them would contain the true
population mean.
(c) (10 pts.) Compute and interpret the effect size [d =
(
X obs - µ H o ) / σ ].
(NA: to be covered later/ the key will be added later)
(d) (15 pts.) Compute the power (1- ") of the test for H1: : = 460.
(NA)
(e) (15 pts.) Provide a statistically valid interpretation of the combined results in (a), (c), and (d). [For
example, would further study with larger sample be needed?, etc.]
(NA)
SECTION III (60 points). The questions below are conceptual in nature. Please think carefully before
you answer. No calculation is necessary to answer the questions.
1. (20 pts.). Comment individually on each of the following statistical case scenarios in terms of
likelihood of committing a type I or II error, statistical and/or scientific/practical significance/importance
of the result, whether further study with larger sample would be needed to clinch the issue in question,
etc. Make statistically relevant arguments.
-----------------------------------------------------------------------------------------case no.
p-value power effect size
-----------------------------------------------------------------------------------------#1
> 0.05 0.40
0.90
#2
< 0.05 0.90
0.10
-----------------------------------------------------------------------------------------(NA)
2. (20 pts.). Elaborate and explain the following statement about the relation between hypothesis testing
and confidence interval estimation:
"Confidence interval estimation is more informative and general than hypothesis testing."
(NA)
3. (20 pts.). The Point of Controversy in Chapter 19 of the text (p. 357) discusses several negative
consequences of research journals refusing to publish statistically nonsignificant results. Give/describe at
least two of the consequences mentioned in the Point of Controversy.
(1) Encourage “false positives” (i.e., statistically significant
results that are actually type I errors will get published).
(2) Cheating and fudging (i.e., “massage” observed data so that
statistically significant results are obtained).