With regard to intelligence scores, at 95% confidence level, there is significant evidence to conclude that violent offenders are less intelligent than property offenders

Step-by-step explanation:

H_a: Violent offenders are less intelligent than property offenders

H_o: Violent offenders and property offenders do not differ significantly with regard to intelligence scores

Test statistic can be found using the formula

z= $\frac{X-Y}{\sqrt{\frac{s(x)^2}{N(x)}+\frac{s(y)^2}{N(y)}}}$ where

X is the mean IQ score of property offenders (96)

Y is the mean IQ score of violent offenders (88)

s(x) is the sample standard deviation of property offenders (8.5)

s(y) is the sample standard deviation of violent offenders (7.5)

N(x) is the sample size for property offenders (225)

N(y) is the sample size for violent offenders (200)

then z= $\frac{96-88}{\sqrt{\frac{8.5^2}{225}+\frac{7.5^2}{200}}}$ ≈10.3

One tail p-value of the test statistic is < 0.00001

Since p-value<0.05 (significance level) we reject the null hypothesis.

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3 years ago