Question

tople who had recently been released from a jail by posting bail were asked how long in Jail before being released. The answers were recorded in days. The data follows: 6.4, 12.1, 1.8, 10.0, 4.5, 0.7, 3.9, A) Find an approximately 95% confidence interval for the mean time to post bail for this jail using a non-parametric method learned in class. B) Find a confidence interval for the mean time to post bail for this jail using a parametric method with the same level of confidence as in part A above. C) Which interval is wider? Would you say the two intervals are comparable? Why or why not?

Answer 1

a)

x<-с (6 . 4, 12 . 1 , 1 . 8, 10,4.5,0.7,3.9) wilcox. tes native="two. sided", conf. int > t (x,alter T) > = Wilcoxon signed rank test data: x V 28, p-value 0.01563 alternative hypothesis: true location is not equal to o 95 percent confidence interval: 1.8 10.0 sample estimates: (pseudo)median 5.4

95% confidence interval (1.8 , 10)

b)

> t.test (x,alt ernative-"two.sided") One Sample t-test data: x t3.5633, df -6, p-value0.01188 alternative hypothesis: true mean is not equal to 0 95 percent confidence interval: 1.763456 9.493687 sample estimates mean of x 5.628571

95% confidence interval (1.763456 , 9.493687) $\simeq$ (1.8 , 9.5)

c)

The 95% confidence intervals for non parametric and parametric distribution is same.