Question 1197125: An extract of a study conducted about the effects of a special class designed to aid students with
verbal skills is given below:
Each child was given a verbal skill 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 µ for Y is equal to 0, the class has no effect, on the average. For the four children in the
study, the observed values of Y are 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 statistical software package:
Variable Number of cases Mean Standard Deviation Standard Error
Y 4 4.000 2.000 1.000
1.1.1 Set up the null and alternative hypotheses. (4)
1.1.2 Calculate the test statistic, and indicate whether the P-value was below 0.05, based on
using the appropriate table. (7)
1.1.3 Make a decision, using α = .05. Interpret. (4)
1.1.4 If the decision in (1.1.3.) 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?
(3)
1.1.5 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.
(3)
1.2 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 non-vegetarian students and
a mean of 2.22 and standard deviation of .67 for the 20 vegetarian students.
1.2.1 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. (4)
1.3 When we use statistical software to compare the means with a significance test, we obtain the
following printout:
Variance T DF Prob>|T|
Unequal 2.9146 41.9 0.006
1.3.1 Interpret the P-value, in context, based on its definition. (Note: You are not being asked
to make a decision at some α-level.) (5
Answer by ikleyn(52780)   (Show Source):
You can put this solution on YOUR website! .
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