Perform the required hypothesis test at the 5% significance level. Determine and
ID: 3312066 • Letter: P
Question
Perform the required hypothesis test at the 5% significance level.
Determine and state the type of test that should be performed to answer the above question (two sample t-test, paired t-test, or ANOVA).
State the null and alternative hypotheses.
Use StatCrunch or SPSS software to perform the hypothesis test. (NOTE: If you choose two sample t-test for this problem, assume that the standard deviations of the two groups are equal and it is appropriate to use pooled t procedures.)
What is the value of the test statistic that you obtained from the software? What is the p-value obtained from the software? What is your conclusion?
10.129 Doing Time. The Federal Bureau of Prisons publishes data in Prison Statistics on the times served by prisoners released from federal institutions for the first time. Independent random samples of released prisoners in the fraud and firearms offense categories yielded the following information on time served, in months. Fraud Firearms 3.6 17.9 25.5 23.8 5.3 5.9 10.4 17.9 10.7 7.0 18.4 21.9 8.5 13.9 19.6 13.3 11.8 16.6 20.9 16. SCExplanation / Answer
we shall analyse this using the open source statistical package R
The hypothesis is
H0 : the mean time served for fraud is not less than that for firearms offenses
H1 : the mean time served for fraud is less than that for firearms offenses
fraud <- c(3.6,5.3,10.7,8.5,11.8,17.9,5.9,7,13.9,16.6)
firearms <- c(25.5,10.4,18.4,19.6,20.9,23.8,17.9,21.9,13.3,16.1)
t.test(fraud,firearms,alternative = "less",conf.level = 0.95)
The results are
t.test(fraud,firearms,alternative = "less",conf.level = 0.95)
Welch Two Sample t-test
data: fraud and firearms
t = -4.0599, df = 17.947, p-value = 0.0003694
alternative hypothesis: true difference in means is less than 0
95 percent confidence interval:
-Inf -4.96056
sample estimates:
mean of x mean of y
10.12 18.78
as the p value is less than 0.05 , hence we reject null hypothesisin favor of alternate hypothesis to conclude that
the mean time served for fraud is less than that for firearms offenses