The proportion of roosters kept within a farm for certain species is 0.23. Suppose a group of researchers randomly samples 41 farms raising this species, counts the number of roosters, and records the...

Extracted text: The proportion of roosters kept within a farm for certain species is 0.23. Suppose a group of researchers randomly samples 41 farms raising this species, counts the number of roosters, and records the sample proportion of roosters. They repeat this 1200 times, and build a distribution of sample proportions. (a) What is this distribution called? Sampling Distribution 8. (b) Would you expect the shape of this distribution to be symmetric, right skewed, or left skewed? Symmetric e (c) Calculate the standard error of this distribution. Round answer to four decimal places (d) Suppose the researchers budget is reduced and they are only able to collect random samples of 10 farms. The sample proportion of roosters is recorded, and we repeat this 1200 times, and build a new distribution of sample means. What is the standard error of this new distribution? Round answer to four decimal places