Does Chemical Treatment Effectively Reduce Contamination Levels in Waterbodies?

  • Thread starter joemama69
  • Start date
  • Tags
    P-value
Best of luck with your studies.In summary, a two-sample z-test was conducted to compare the proportion of high contamination levels (HCL) in two different waterbodies before and after treatment. The null hypothesis was that there was no difference in the proportion of HCL before and after treatment, while the alternative hypothesis was that the proportion had decreased after treatment. The test statistic was calculated to be 1.027 and the p-value was 0.152, which was greater than the significance level of 0.05. Therefore, the null hypothesis could not be rejected and it was concluded that there was not enough evidence to suggest a decrease in the proportion of HCL in the first waterbody after treatment. Further considerations
  • #1
joemama69
399
0

Homework Statement



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.


Homework Equations





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
 
Physics news on Phys.org
  • #2
or should we use the lower tail and use p-value = zvalue?

Thank you for your post. I would like to address your question and provide my thoughts on your solution attempt.

Firstly, it is important to define the null and alternative hypotheses for your experiment. In this case, the null hypothesis (H_0) would be that there is no difference in the proportion of HCL in the first waterbody before and after treatment. The alternative hypothesis (H_1) would be that the proportion of HCL has decreased after treatment.

Next, we need to determine the appropriate test statistic to use. Since we are comparing two proportions, the appropriate test statistic would be the two-sample z-test. This test compares the difference between two proportions to the expected difference under the null hypothesis.

Using your notation, the test statistic can be calculated as follows:

z = (P_1 - P_2) / √[(P(1-P)) / (1/n_1 + 1/n_2)]

Where P is the pooled proportion, calculated as (x_1 + x_2) / (n_1 + n_2). In this case, P = (16 + 12) / (69 + 69) = 0.2029.

Plugging in the values, we get z = (0.2319 - 0.1739) / √[(0.2029(1-0.2029)) / (1/69 + 1/69)] = 1.027.

Next, we need to calculate the p-value associated with this test statistic. Since we are interested in whether the proportion has decreased (P_1 > P_2), we use the upper tail of the standard normal distribution. This gives us a p-value of 0.152, which is greater than the commonly used significance level of 0.05.

Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the proportion of HCL in the first waterbody has decreased after treatment.

In summary, your approach was generally correct, but there were a few minor errors. It is important to carefully define the null and alternative hypotheses and use the appropriate test statistic and p-value. Additionally, it is important to interpret the results in the context of the experiment and consider any potential limitations or confounding factors.

I hope this helps clarify your understanding
 

FAQ: Does Chemical Treatment Effectively Reduce Contamination Levels in Waterbodies?

1. What is a p-value and why is it important in scientific research?

A p-value is a statistical measure that helps scientists determine the significance of their findings. It represents the probability of obtaining results as extreme as what was observed, assuming that the null hypothesis is true. In other words, it helps determine the likelihood that the observed results are due to chance. A low p-value (usually less than 0.05) indicates that the results are unlikely to be due to chance and are therefore considered statistically significant.

2. How is the p-value calculated from two tests?

The p-value from two tests is usually calculated by combining the p-values from each individual test using a statistical method called meta-analysis. This involves taking into account the sample sizes and effect sizes of each test to determine an overall p-value for the combined results.

3. Can the p-value be interpreted as the probability that the null hypothesis is true?

No, the p-value should not be interpreted as the probability that the null hypothesis is true. It only represents the probability of obtaining the observed results if the null hypothesis is true. Therefore, a low p-value does not necessarily mean that the null hypothesis is false, but rather that the observed results are unlikely to be due to chance.

4. What is the significance level and how is it related to the p-value?

The significance level (usually set at 0.05) is the threshold at which a p-value is considered statistically significant. If the p-value is less than the significance level, then the results are considered statistically significant and the null hypothesis is rejected. On the other hand, if the p-value is greater than the significance level, then the results are not considered statistically significant and the null hypothesis is not rejected.

5. Can the p-value be used to determine the magnitude or importance of the effect?

No, the p-value only indicates the likelihood of obtaining the observed results by chance. It does not provide information about the magnitude or importance of the effect. To determine the magnitude of the effect, scientists must look at other measures such as effect size or confidence intervals.

Similar threads

Back
Top