Determine the test statistic

Reference no: EM131002378

In the table below, X1 is a random sample of 20 observations from an expo- nential population with parameter β = 1.44, so that the median, η = 1. X2 is the same data set plus a constant, 0.6, and random Gaussian noise with mean μ = 0 and standard deviation σ = 0.15.

X1 1.26968	X2 1.91282	X1 1.52232	X2 2.17989
0.28875	1.13591	1.45313	2.11117
0.07812	0.72515	0.65984	1.45181
0.45664	1.19141	1.60555	2.45986
0.68026	1.34322	0.08525	0.43390
2.64165	3.18219	0.03254	0.76736
0.21319	0.88740	0.75033	1.16390
2.11448	2.68491	1.34203	2.01198
1.43462	2.16498	1.25397	1.80569
2.29095	2.84725	3.16319	3.77947

(i) Consider the "postulate" that the median for both data sets is η0 = 1 (which, of course, is not true). Generate a table of signs, Dmi , of deviations from this postulated median.

(ii) For each data set, determine the test statistic, T +. What percentage of the observations in each data set has plus signs? Informally, what does this indicate about the possibility that the true median in each case is as postulated?

Reference no: EM131002378

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