A random sample of 230 police officers in New York averaged 345 tickets a year w

Question

A random sample of 230 police officers in New York averaged 345 tickets a year with a standard deviation of 15. A random sample of 183 police officers in Vermont had 365 tickets a year with a standard deviation of 14. Construct a 95% confidence interval for the difference between the two means. A random sample of 150 police officers in New Jersey averaged 466 tickets a year with a standard deviation of 22. A random sample of 300 police officers in Maine had 350 tickets a year with a standard deviation of 24. At the .05 level, test the claim that more officers in New Jersey plan to retire.

Explanation / Answer

1)here

therefore std error =(s12/n1 +s22/n2)1/2 =1.4315

also for 95% CI, z =1.96

hence confidence interval of difference of mean =(x1-x2) +/- z*std error =-22.806 ; -17.194

2)here

therefore std error =(s12/n1 +s22/n2)1/2 =2.269

hence zstat =(X1-X2)/std error =51.132

for which p value =0.00

as p value is higher then 0.05 level, hence we reject that mean is equal . and accept that new jersey policemen has higher amount of work with respect to giving ticket and more prone to retire early.

std deviation(S) S1 15.000 S2 14.000 sample size n1 230 n2 183 mean X1 345.000 X2 365.000

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