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        Psychology 406

        Assignment \#5


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1) Hays --- Chapter 7, \#8, \#16, \#20


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2) Assume that Randy Researcher is doing his Master's thesis and has
developed a test of reading readiness for his experiment.  He
believes that the scores he gets from independent observations on
children are N($\mu$, 4).  In other words, he knows the variance but
not the mean.

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a) Randy wants to test the hypothesis $\mathrm{H}_{o}$: $\mu$ = 5
versus  $\mathrm{H}_{1}$: $\mu$ = 8.  If he has 9 independent
observations (i.e., a random sample of 9 observations from the
population of interest), what is the cutoff point for a significant
result at $\alpha$ = .05 ($\alpha$ = .01)?  What is the
corresponding power for the test at $\alpha$ = .05 ($\alpha$ = .01)?

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What would you say if he observed a sample mean of 4, or 5.5, or
7.5?

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b) If Randy wishes to test $\mathrm{H}_{o}$: $\mu \le$ 5 versus
$\mathrm{H}_{1}$: $\mu > 5$, what is the cutoff value for the mean
of 9 independent observations for $\alpha$ = .05 ($\alpha$ = .01)?
What is the cutoff value's relationship to your answer in (a)? Can
you say anything about power?

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c) Find the critical values (cutoff points) in a two-sided test of
$\mathrm{H}_{o}$: $\mu =$ 5 versus $\mathrm{H}_{1}$: $\mu \ne 5$
($\alpha$ = .01 and .05) for the sample of 9 observations.  What is
the relationship of the rejection region calculated here to the
rejection region for the null hypothesis in (a)?  Which of the two
regions (i.e., calculated in (a) or (c)), would you prefer and when?

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3)  Suppose you flip a coin twenty times and get 18 heads.  Would
you reject the hypothesis that the coin is ``fair''?  Provide a
p-value. (Hint: Set up a ``null'' hypotheses and an alternative ---
use the normal approximation to the Binomial.  Should your test be
one-tailed or two-tailed?  Why?)
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