It is often said that the criminal sentences given to minority offenders are more severe than those given to whites. You examine how this works in a federal district court. You take a sample of 80 bank robbery cases where the convicted offender was white and a second independent sample of 80 cases where the convicted offender was either African-American or Hispanic. Here's the data that you get: White n₁ = 80 X₁= 67 months S1 = 18 Minority n₂ = 80 X₂ = 73 months $2 = 29

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35
It is often said that the criminal sentences given to minority offenders are more severe than those
given to whites. You examine how this works in a federal district court. You take a sample of 80
bank robbery cases where the convicted offender was white and a second independent sample of
80 cases where the convicted offender was either African-American or Hispanic. Here's the data
that you get:
White
F3
n₁ = 80
X₁= 67 months
S1 = 18
20
Test the null hypothesis that there is no difference between the two groups versus the alternative
hypothesis that white suspects are sentenced on average to fewer months. Use an alpha of 0.05
(one-tailed). You cannot assume that the two population standard deviations are equal (0₁ ± 0₂), so
you are going to be using an independent samples separate variance t-test. Use 155 as your
degrees of freedom.
Your null hypothesis is written as μWhite = μMinority
Minority
n2 = 80
X2 = 73 months
S2 = 29
Your alternative hypothesis is written as uWhite < μMinority
You use your alpha of 0.05 and df of 155 to find your critical value in the t-distribution table. Your
critical t value is -1.658
→
Si
You enter your information into the formula for an independent samples separate variance t-test
, and find that your obtained t-value is -1.56
$
4
co Qu obtained + value is greater than
DOD
DOD
F4
15
%
F5
A
6
F6
&
7
your criticalt valua vou da
F7
8
DII
F8
(
9
DD
F9
0
F10
Transcribed Image Text:35 It is often said that the criminal sentences given to minority offenders are more severe than those given to whites. You examine how this works in a federal district court. You take a sample of 80 bank robbery cases where the convicted offender was white and a second independent sample of 80 cases where the convicted offender was either African-American or Hispanic. Here's the data that you get: White F3 n₁ = 80 X₁= 67 months S1 = 18 20 Test the null hypothesis that there is no difference between the two groups versus the alternative hypothesis that white suspects are sentenced on average to fewer months. Use an alpha of 0.05 (one-tailed). You cannot assume that the two population standard deviations are equal (0₁ ± 0₂), so you are going to be using an independent samples separate variance t-test. Use 155 as your degrees of freedom. Your null hypothesis is written as μWhite = μMinority Minority n2 = 80 X2 = 73 months S2 = 29 Your alternative hypothesis is written as uWhite < μMinority You use your alpha of 0.05 and df of 155 to find your critical value in the t-distribution table. Your critical t value is -1.658 → Si You enter your information into the formula for an independent samples separate variance t-test , and find that your obtained t-value is -1.56 $ 4 co Qu obtained + value is greater than DOD DOD F4 15 % F5 A 6 F6 & 7 your criticalt valua vou da F7 8 DII F8 ( 9 DD F9 0 F10
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