How to Calculate Population Size using Neyman-Pearson Lemma?

  • MHB
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In summary, the conversation discussed the steps taken to calculate the overall population size for a sample. This included creating a data frame of population sizes, calculating proportions of each population size, multiplying these proportions by their corresponding population sizes, and dividing the sum by the total population size of the sample.
  • #1
mathjam0990
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View attachment 5424Here is what I have done so far...

View attachment 5425

I am not sure if I have approached this the correct way. If anyone could help me out by telling me if I am doing this correctly or if not, provide a step by step to show how, that would be great! Thank you.
 

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  • #2
1. First, I created a data frame containing the population sizes for each city in the sample.2. Next, I calculated the proportions of each population size to the total population size for the sample by dividing the population size of each city by the total population size of the sample.3. Then, I calculated the weighted mean population size by multiplying each proportion by the corresponding population size and summing up the results.4. Finally, I divided the sum of the weighted mean population size by the total population size of the sample to get the overall population size for the sample.
 

FAQ: How to Calculate Population Size using Neyman-Pearson Lemma?

What is the Neyman-Pearson Lemma?

The Neyman-Pearson Lemma is a fundamental theorem in statistical hypothesis testing that provides a framework for finding the most powerful test for a given significance level. It is named after Jerzy Neyman and Egon Pearson, who first introduced it in 1933.

How does the Neyman-Pearson Lemma work?

The Neyman-Pearson Lemma works by considering two hypotheses: the null hypothesis and the alternative hypothesis. It then determines the likelihood ratio of the two hypotheses and compares it to a predetermined threshold called the critical value. If the likelihood ratio is greater than the critical value, the null hypothesis is rejected in favor of the alternative hypothesis.

What is the significance level in the Neyman-Pearson Lemma?

The significance level in the Neyman-Pearson Lemma is the probability of rejecting the null hypothesis when it is actually true. It is typically denoted by the symbol alpha and is chosen by the researcher before conducting the test. A lower significance level indicates a higher level of confidence in the results.

What is the power of a test in the Neyman-Pearson Lemma?

The power of a test in the Neyman-Pearson Lemma is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is actually true. It is denoted by the symbol beta and is equal to 1 minus the probability of a Type II error (failing to reject the null hypothesis when it is false). A higher power indicates a more sensitive test.

In what situations is the Neyman-Pearson Lemma most useful?

The Neyman-Pearson Lemma is most useful in situations where there is a clear distinction between the null and alternative hypotheses, and where a small probability of a Type I error (rejecting the null hypothesis when it is true) is acceptable. It is commonly used in scientific research, quality control, and other fields where rigorous testing is needed.

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