N = 1 Hypothesis Testing Exercise: What is Geri’s Gender?
At a costume party you are introduced to a graduate student named Geri Jones. You are
uncertain regarding Geri's gender, given the costume and all. During the course of the evening, a
weight-guessing game is played. When Geri plays the game, you take notice of the fact that e's
weight is revealed to be 148 lb. You happen to remember the details of some statistics that one of
your PSYC 6430 classmates reported when presenting her Personal Data Set homework. She
reported that the mean weight of female graduate students in her sample was 123.36, with a
standard deviation of 14.63. Consider Geri's weight to represent a sample of one score randomly
drawn from a normally distributed population of weights with a mean of 123.36 and a standard
deviation of 14.63. That is, your null hypothesis is that Geri's weight was randomly drawn from a
population of weights identical to that of female graduate students (in other words, Geri is a
woman).
1. Draw a normal curve representing the sampling distribution under the null hypothesis.
Draw a vertical line bisecting it at the mean, and write in below that line the value 123.36, which is
the mean of the sampling distribution under the null hypothesis.
2. After pondering the relative risks associated with Type I and Type II errors, you decide
to employ a .05 criterion of statistical significance. That is, if your p value comes out to be less
than or equal to .05, you shall reject the null hypothesis.
3. You also decide that a one-tailed test is appropriate here. If Geri's weight came out to
be much lower than expected for a woman, you would not then conclude that e is a man, but if it
came out to be much more than expected for a woman, then you would conclude that e is a man.
4. Now draw a vertical line at that point representing the mean of your sample, 148.
Shade the area to the right of that line. This shaded area represents p, the probability of obtaining
results as or more discrepant with the null hypothesis than is the result you obtained, assuming
that the null hypothesis is true. Compute the z-score (your test statistic) that represents this
sample of 148 under the null hypothesis, and then use the normal curve table to find p.
5. Compare your obtained p with the criterion of significance and draw your conclusion
regarding whether or not Geri is a woman.
6. If you had used a two-tailed test, how heavy would Geri have to be before you decided
that e was not a woman? How light would e have to be before you decided e was not a woman
(but rather something that weighs less than do women)?
7. Suppose that you learn that the scale was off by 3 lb, and Geri's weight is actually 145
lb. Recompute z, p, and draw your conclusion again.
8. Suppose that you decide to test the null hypothesis that Geri is a man, that is, that e's
weight (145 lb) is a random sample of one score from the population of weights of male graduate
students, which is known to be normally distributed with a mean of 163.76 and a standard
deviation of 17.65. Compute z, p, and draw your conclusion.
9. Using the results of the two analyses above (# 7 and # 8), what is your final conclusion
about Geri's gender?
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Copyright 2000, Karl L. Wuensch - All rights reserved.
HW4-Geri.doc