(10 pts total) A group of criminologists compared the homicide rates in 7 states
ID: 3362425 • Letter: #
Question
(10 pts total) A group of criminologists compared the homicide rates in 7 states with capital punishment to the homicide rates in 7 states without capital punishment. Obviously states differ in many ways that can impact homicide rates, so they used a matched samples design to deal with several of these extraneous variables. Specifically, they matched 7 death penalty states to 7 non-death penalty states in terms of geographic similarity and other critical demographic and socioeconomic variables (e.g., Nebraska was paired with lowa, New Hampshire with Vermont, South Dakota with North Dakota, etc.). The death penalty states (M-3.09, s 1.51) and the non-death penalty states (M-2.99,s 1.88) were used to compute difference scores (MD-0.10, s = 0.90). The researchers now want to use estmiation procedures to draw conclusions. For the procedures below think very carefully about the design of the study and what this means for the type of test you should use and the degrees of freedom. Also pay close attention to which means and standard deviations should be used. a. What is the estimation formula for this type of design? (2 pts) b. Compute the point estimate for the mean difference. (I pt) c. Compute the 90% confidence interval around the mean difference. (2 pts) d. Compute the 99% confidence interval around the mean difference. (2 pts) Consider which of the three estimates above (b, c, or d) has the most precision and which offers the greatest degree of confidence. How does the degree of confidence relate to the precision of the estimate? (I pt) e.Explanation / Answer
4
we are given that
mean = 7.23
sd = 1.44
n = 16
we know that the confidence interval is given as
mean +- z*sd/sqrt(n) , here z is 1.96 for 95% CI from the z table
so we put the values in the equation as
7.23 +- 1.96*1.44/sqrt(16)
6.52 , 7.93
b)
This means that we are 95% confident that the true value of the mean would lie in the interval
6.52 and 7.93
c)As confidence interval is 6.52 and 7.93 , it does not include 5 , hence A wins and the conclusion is that the mean for Pullman is higher than the national average
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