Estimating Sample Size
1. A school research director notes that the norm for an eighth-grade reading
test is 80.0. He would like to know whether his eighth-grade students may
be considered to perform at this level, or whether they differ. He feels
that the risk of making a Type I error should be .05, and that a risk of
.10 of making a Type II error would be acceptable. From the data of the
norm group, he estimates that the standard deviation of reading test scores
is 12.0, and he feels that if the mean of his students is 6 points (or more)
away from the norm, it would be important to know it. State the hypothesis
and the alternative hypothesis appropriate to his interest. What sample
size should be select to
test this hypothesis?
2. In reference to the previous problem, what should sample size be if
the research director felt that (a) the risk of a Type II error should be
.05? (b) it was important to know if the mean of his students was 3 points
(or more) away from the norm? (c) he would take action only if his students
were significantly below the norm. (Regard each of the parts to this question
to be independent.)
3. A psychologist wonders whether midsemester warning notions improve performance.
She decides to select a sample of delinquent students and, at random, to
send such notices to half of them and no notice to the other half. Experience
suggests that among such delinquent students the standard deviation is equal
to .30. She decides to adopt an alpha equal to .05, and a desired
power of .95. If the difference between warned and unwarned students is
as great as .075 grade point, she would want to know it. State the hypothesis
and alternate hypothesis appropriate to her interest. What should the size
of each sample be to test this hypothesis?
4. For the previous problem, what should the sample size be if the psychologist
felt that (a) she should choose alpha equal to .01 and power equal to .80?
What should the sample size be if it was important to know if the difference
between the means was .15 point (or more)? What sample size should be selected
if it was only desired to discover if the warning system were different
from the non-warning system, rather than superior to it? Regard each of
the parts of this question to be independent.
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