Final answer:
The sample proportion of samp2 may vary from that of samp1 due to sampling variability, but larger samples yield more accurate estimates of the population proportion. A sample of size 1000 would provide a more accurate estimate than smaller samples due to the law of large numbers.
Step-by-step explanation:
Comparing Sample Proportions and Estimating Population Proportion
When you are dealing with a proportion problem, you are typically looking at categorical data that can be divided into two categories, such as 'Yes or No', 'Success or Failure', etc. This often involves estimating the true population proportion, for example, determining what proportion of the population will vote for a particular candidate or has a college-level education.
The sample proportion of samp2 may or may not be similar to that of samp1, as it is subject to sampling variability. However, by the central limit theorem for proportions, if the samples are large enough, the sample proportions' distribution P' will be approximately normal with mean p and standard deviation sqrt(p*q/n), where p is the population proportion and q is 1 - p.
Taking larger samples tends to yield a more accurate estimate of the population proportion, according to the law of large numbers. Therefore, a sample size of 1000 would generally provide a more accurate estimate than a sample size of 100 or 50, as it better approximates the normal distribution, reducing the standard error of the proportion estimate.
In practice, you would perform a test of two population proportions from independent samples to ascertain if the observed differences are statistically significant or could have occurred due to chance. This involves setting up null and alternative hypotheses and calculating a p-value to make an inference about the population.