Question

Use Wilcoxon Rank-Sum Test, and please SHOW ALL WORK! Using a calculator is fine, but please identify the steps you used in the calculator so I can learn!!!

° The data below lists the amounts of strontium-90 (in millibecquerels, mBa) per gram of calcium in a simple random sample of baby teeth obtained from PA residents and NY residents born after 1979. Use 0.05 level of significance and Wilcoxon Rank-sum Test to test the claim that the median amount od strontium-90 from PA is the same as the median from NY PA: 155, 142, 149, 130, 151, 163, 151, 142, 156, 133, 138, 161 NY: 133, 140, 142, 131, 134, 129, 128, 140, 140, 140, 137, 143

Answer 1

Wilcoxon Rank-Sum Test,

Ho: median difference=0

H1: median difference ╪ 0

sample 1	sample 2	rank for sample 1	rank for sample 2
155	133	21	5.5
142	140	15	11.5
149	142	18	15
130	131	3	4
151	134	19.5	7
163	129	24	2
151	128	19.5	1
142	140	15	11.5
156	140	22	11.5
133	140	5.5	11.5
138	137	9	8
161	143	23	17

sample 1

sample size , n1 = 12

sum of ranks , R1 = 194.5

sample 2

sample size , n2 = 12

sum of ranks ,R2 = 105.5

R=sum of ranks for smaller sample size =194.5

Observe that both sample sizes are greater than 10, then we can use normal approximation. The following z-statistic will be used.

mean ,µ = n1(n1+n2+1)/2 = 150

std dev,σ = √(n1*n2*(n1+n2+1)/12) =17.3205

Z-stat = (R - µ)/σ = 2.5692

P-value = 0.0102

Conclusion:                            P-value<α , Reject null hypothesis

so, there is enough evidence to reject the claim at α=0.05