Public Policy and Political Science Juvenile courts in all states maintain caref

Question

Public Policy and Political Science Juvenile courts in all states maintain careful records for cases, including demographics, charges, and dispositions. One variable of interest for repeat offenders is the number of days since the last offense (or arrest). A random sample of repeat offenders appearing in juvenile court was obtained for three states. The number of days since the last offense was recorded for each, and the summary statistics are given in the table below. Assume the underlying distribution of days since the last offense is normal for each state. Find a 99% confidence interval for the true mean number of days since the last offense for repeat offenders in each state. Using your answers to part (a), is there any evidence to suggest the true mean number of days since the last offense in Ohio and California is different? How about California and Massachusetts? Justify each answer.

Explanation / Answer

a.
i.
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=180.6
Standard deviation( sd )=37.8
Sample Size(n)=17
Confidence Interval = [ 180.6 ± t a/2 ( 37.8/ Sqrt ( 17) ) ]
= [ 180.6 - 2.921 * (9.168) , 180.6 + 2.921 * (9.168) ]
= [ 153.821,207.379 ]
ii.
Mean(x)=162.7
Standard deviation( sd )=25.2
Sample Size(n)=29
Confidence Interval = [ 162.7 ± t a/2 ( 25.2/ Sqrt ( 29) ) ]
= [ 162.7 - 2.763 * (4.68) , 162.7 + 2.763 * (4.68) ]
= [ 149.77,175.63 ]
iii.
Mean(x)=115.3
Standard deviation( sd )=17.6
Sample Size(n)=22
Confidence Interval = [ 115.3 ± t a/2 ( 17.6/ Sqrt ( 22) ) ]
= [ 115.3 - 2.831 * (3.752) , 115.3 + 2.831 * (3.752) ]
= [ 104.677,125.923 ]

b.
i.the true mean number of days
since the last offense in Ohio and California is n't different
ii.
California and Massachusetts are diffrent

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