Question

Describe a real-world business situation that could be addressed by collecting and analyzing a set of data using the t-test. What open source would you use to collect that data?

Answer 1

Has Support for Capital Punishment Changed over Time? The General Social
Survey (GSS) has been collecting demographic, behavioral, and attitudinal information since 1972
to monitor changes within the US and to compare the US to other nations. Support for the capital
punishment (the death penalty) in the US is shown in 1974 and in 2006 in the two-way table below.
Find a 95% confidence interval for the change in the proportion supporting capital punishment
between 1974 and 2006. Is it plausible that the proportion supporting capital punishment has not
changed?
Year Favor Oppose Total
1974 937 473 1410
2006 1945 870 2815
Solution
Letting ˆp1 and ˆp2 represent the proportion supporting capital punishment in 2006 and 1974, re-
spectively, we have
pˆ1 = 1945 = 0.691 and ˆp2 = 937 = 0.665The sample sizes are both large, so it is reasonable to use a normal distribution. For 95% confidence
the standard normal endpoint is z
∗ = 1.96. This gives
(ˆp1 − pˆ2) ± z
∗
·
s
pˆ1(1 − pˆ1)
n1
+
pˆ2(1 − pˆ2)
n2
(0.691 − 0.665) ± 1.96∗
·
r
0.691(1 − 0.691)
2815
+
0.665(1 − 0.665)
1410
0.026 ± 0.030
−0.004 to 0.056
We are 95% sure that, between 1974 and 2006, the percent change in support of the death penalty
is between a decrease of 0.4% and an increase of 5.6%. Since a difference of zero (no change) is
within this interval, it is plausible that there have been no change in support or opposition to the
death penalty in this 22-year period.