Please discuss, elaborate, and reflect on the following:
1. Compare and contrast random samples, research samples, and biased samples
2. Distinguish between a sampling distribution and a frequency distribution.
3. Explain the Central Limit Theorem.
Show your work and explain your results to answer each question. Don’t write just a number.
1. Use a random number table to draw a random sample with N = 8 from the following scores.
21, 31, 17, 13, 02, 09, 57, 26, 72, 140, 27, 27, 27, 21, 13, 57, 43, 22, 18, 19, 18, 18, 18, 23, 25, 66, 75, 89, 99, 112.
2. Calculate the standard error of the mean for a sample of 8 for the population in Problem #1. The summation of x = 1205 and summation of x to the power of two = 82091
3. A teacher was interested in the mathematical ability of graduating high school seniors in her state. She gave a 32-item test to a random sample of 75 seniors from her state with the following results: The summation of x = 1275 and summation of x to the power of two= 23525. Establish a 95% confidence interval about the mean, and write a sentence that explains the interval you found to a high school principal.