STAT170 Workshop Notes prepared by Nan Carter for Numeracy ...

QUESTION 1: The Chapin Social Insight Test is a psychological test designed
to measure how accurately the subject appraises other people. The possible
scores on the test range from 0 to 41. During the development of the Chapin
Test, it was given to several groups of people. Here are the results for male and
female students majoring in the liberal arts:
Group Sex N X-bar S.D.
1 Male 133 25.34 5.05
2 Female 162 24.94 5.44
Do these data support the contention that female and male students differ in
average social insight?
The variable is a score on a psychological test. It is reasonable to assume the
variable, score, is normally distributed.
Do these data support the contention that female and male students differ in
average score?
CHECKS: sp = 5.2679; SE(y1bar – y2bar) = 0.6164; t = 0.649; df = 293; pvalue
> 0.05; no.
METHOD Two independent random samples: do the samples come from
populations with the same mean?
Population 1 male 2 female
Mean μ1 μ2
Standard deviation σ1 σ2
Sample size n1 133 n 2 162
Sample mean y1bar 25.34 y2bar 24.94
Sample SD s1 5.05 s 2 5.44
Null hypothesis H0: μ1 = μ2
Assumptions:
• the populations are both normal
• the standard deviations are equal, or in symbols: σ1 = σ 2;
• to check this second assumption use:
smax / s min < about 2.
The value of the t-statistic is given by
y1bar – y2bar
t = __________________ where
SE(y1bar – y2bar)
SE(y1bar – y2bar) = sp √( 1/n1 + 1/n2) and
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Nan Carter: workshop notes prepared for Numeracy Centre Macquarie University.