P-Value from two tests

1. Apr 13, 2013

joemama69

1. The problem statement, all variables and given/known data

Binomial Proportion ......

In a laboratory experiment, water samples from different waterbodies were examined to check the levels of contamination and were subsequently treated with chemicals for reducing the contamination levels.

In one waterbody exposed to industrial pollution, 16 out of 69 sample containers developed High Contamination Level [HCL].
In a second waterbody, 20 out of 72 sample containers were affected by HCL.

All the samples from both the waterbodies were treated with chemicals for reduing the HCL. It was subsequently revealed that 12 out of 69 from the first lot and 15 out of 72 from the second lot still retained HCL.

(i) Test H_01 : First waterbody HCL has been reduced after chemical treatment.

2. Relevant equations

3. The attempt at a solution

P_1 = 16/69 = 0.2319, P_2 = 12/69 = 0.1739, Test P_1 > P_2

P = (x_1 + x_2)/(n_1+n_2) = (16+12)/(69+69) = 0.2029

Z = (P_1 - P_2)/sqrt(P(1-P)(n_1 + n_2)/(n_1*n_2) = (0.2319 - 0.1739)/sqrt(0.2029(1-0.2029)(69+69)/(69*69) = 0.8471,

looking it up on the z-table gives 0.8023,

p-value = 1-.8023 = 0.1977 = about 20% so we accept the null and declair little to no change has been made...

Is it correct to test if the contamination has gone down (P_1>P_2), then we use the upper tail and have use p-value = 1-zvalue