z-test for means
1. Suppose a researcher replicates the study from the class (Martin’s data) in which the mean IQ of longterm alcoholics was compared to the norm. In this attempt at replication, the researcher samples 20
different participants and measures their IQ with the Ravens (normed mean = 100, std. dev. = 16). Do
the current results support his hypothesis that long-term alcoholics will, on average, have lower IQs
than the general population?
105, 100, 100, 115, 100, 105, 120, 120, 100, 105, 105, 110, 95, 110, 110, 95, 109, 100, 125, 120
a. Compute the descriptive statistics for the data (mean, median, mode, SS, s2, and s). You do not
have to show your work; in other words, you can use your calculator to compute these values.
b. Do the data support the researcher’s hypothesis? Use NHST as we did in class and draw a
conclusion:
A. Write your hypotheses in 3-valued logic form.
B. Sketch a standard normal distribution and set up the rejection region using an a priori pvalue (that is, alpha) equal to .05 and appropriate critical values.
C. Compute zobs using the formula from class.
D. Judge whether or not zobs falls in the rejection region and state if your result is statistically
significant or nonsignificant.
E. State your conclusion in words (e.g., “It appears that the population mean…”).
F. Compute pobs by looking up your zobs in the z-table and doubling the value.
G. Compute and interpret the effect size (small, medium, large using Cohen’s conventions)
H. Compute and interpret the confidence interval (narrow, middling, wide based on the
standard deviation)
c. Could the conclusion regarding the results be wrong? Explain why this is the case.
2. You hypothesize that college students will, on average, show higher levels of depression on a well-known
depression scale. This well-known scale has been normed to a mean of 20 and standard deviation of 10 (the
scores can range from 0 to 40; high scores indicate more depression). From a sample of 28 students you obtain
the following depression scores:
20, 18, 15, 5, 25, 10, 8, 0, 2, 27, 4, 5, 4, 4, 10, 16, 25, 18, 10, 12, 12, 4, 24, 18, 10, 13, 8, 10
Do the data support your hypothesis? Use an alpha level of .05 and work through the steps in NHST outlined in
the problem above.
3. You hypothesize that veterans returning from recent combat will, on average, show higher levels of anxiety on a
well-known anxiety scale. This well-known scale has been normed to a mean of 21 and standard deviation of 7
(the scores can range from 0 to 63; high scores indicate more anxiety). From a sample of 15 veterans you obtain
the following anxiety scores:
40, 32, 21, 20, 55, 45, 31, 28, 27, 45, 50, 40, 33, 31, 25
Do the data support your hypothesis? Use an alpha level of .01 and work through the steps in NHST outlined in
the problem above. Note here you’ll have to look up a new z-critical value from the z-table based on the alpha
of .01.