Null Hypothesis Waterbody - Environmental Statistics

[joemama69]

Homework Statement

Past study in a contaminated waterbody has revealed that the percentage contamination level of the surface water has been determined at 24.75%

a)Based on a study of a random sample of 40 containers of the same size, it is observed that the sample percentage of contaminted containers is 21.65%. Does it indicate that some efforts have gone into cleaning of the waterbody?

b)An independant organization conducted a similar parallel study at it revealed that the percentage contaminatin level was 22.78% based on a sample size of 25. Does this corroborate the decision reached in question A.

c)Can you combine the two data sets and come up with a bettter understanding about the level of contamination of the waterbody.

Homework Equations

I believe we use P +/- 1.645 sqrt((P(1-P)/n) with a confidence level of 95%

The Attempt at a Solution

See attached pdf . Does anyone see any issues with my calculations? Just realized my 95% CI z value should be 1.645 not 1.654. Other than that, any issues?

 

[mighty2000]

Thank you for sharing your calculations and seeking feedback on your approach. I would like to provide some insights on your questions and offer some suggestions.

a) Based on the sample data provided, it does not necessarily indicate that efforts have gone into cleaning the waterbody. The sample data only represents a small portion of the entire population, and it is possible that the percentage of contaminated containers could vary in different areas of the waterbody. It would be more accurate to conduct a larger sample study and compare the results before drawing any conclusions about the effectiveness of cleaning efforts.

b) The independent organization's study does not necessarily corroborate the decision reached in question A, as the sample sizes and results are different. It is possible that the two studies were conducted in different areas of the waterbody or at different times, leading to different results. However, it does provide additional information that can be used in conjunction with the first study to gain a better understanding of the contamination level.

c) Combining the two data sets can provide a better understanding of the contamination level of the waterbody. However, it is important to note that the two studies were conducted independently and may have different methodologies and sample sizes, which could affect the accuracy and reliability of the combined data. It would be best to carefully examine the data and consider any potential limitations before making any conclusions.

In terms of your calculations, it seems that you have used the correct formula for calculating the confidence interval. However, it is always good practice to double-check your calculations and ensure that the correct values are used. Additionally, it may be helpful to provide a visual representation of the data, such as a graph or chart, to better illustrate the results and facilitate comparison between the two studies.

I hope this helps and provides some guidance on how to approach this problem. Keep up the good work in your scientific endeavors!