Statistics 101 Sample questions: EXAM 2
1. A study was conducted of the effects of a special class designed to aid students
with verbal skills. Each child was given a verbal skills test twice, both before
and after completing a 4-week period in the class. Let Y= score on exam at
time 2 - score on exam at time 1. Hence, if the population mean µfor Yis equal
to 0, the class has no effect, on the average. For the four children in the study,
the observed values of Yare 8-5=3, 10-3=7, 5-2=3, and 7-4=3 (e.g. for the first
child, the scores were 5 on exam 1 and 8 on exam 2, so Y= 8-5=3). It is planned
to test the null hypothesis of no effect against the alternative hypothesis that
the effect is positive, based on the following results from a computer software
package:
Number
Variable of Cases Mean Std. Dev. Std. Error
Y 4 4.000 2.000 1.000
a. Set up the null and alternative hypotheses.
b. Calculate the test statistic, and indicate whether the P-value was below
0.05, based on using the appropriate table.
c. Make a decision, using α= .05. Interpret.
d. If the decision in (c) is actually (unknown to us) incorrect, what type of
error has been made? What could you do to reduce the chance of that
type of error?
e. True or false? When we make a decision using α=.05, this means that if
the special class is truly beneficial, there is only a 5% chance that we will
conclude that it is not beneficial.
2. For a random sample of Harvard University psychology majors, the responses
on political ideology had a mean of 3.18 and standard deviation of 1.72 for 51
nonvegetarian students and a mean of 2.22 and standard deviation of .67 for
the 20 vegetarian students.
a. Defining appropriate notation, state the null and alternative hypotheses
for testing whether there is a difference between population mean ideology for
vegetarian and nonvegetarian students.
b. When we use software to compare the means with a significance test, we
obtain the printout
Variances T DF Prob>|T|
---------------------------------------
Unequal 2.9146 41.9 0.006
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