Question

tal Score: Save Submit Assignment for Gra Submit Assian Exercise 07.17 Algorithmic Question 4 of Check My Wor eBook Suppose a random sample of size 42 is selected from a population with o = 11. Find the value of the standard error of the meanin each of the following cases (use the finite population correction factor if appropriate). a. The population size is infinite (to 2 decimals). b. The population size is N = 50,000 (to 2 decimals). c. The population size is N = 5000 (to 2 decimals). d. The population size is N = 500 (to 2 decimals). ® Hide Feedback Incorrect Check My Work

Answer 1

a)
If the population size is infinite, then the standard error of the mean = Standard deviation / n^(1/2)
= 11 / 42^(1/2)
= 11 / 6.4807407
= 1.70

b)
If the population size (N) = 50,000 then the standard error of the mean = (Standard deviation / n^(1/2)) * ((N - n) / (N - 1))^(1/2)
= (11 / 42^(1/2)) * ((50,000 - 42) / (50,000 - 1))^(1/2)
= 1.6973 * 0.999589908
= 1.70

c)
If the population size (N) = 5,000 then the standard error of the mean = (Standard deviation / n^(1/2)) * ((N - n) / (N - 1))^(1/2)
= (11 / 42^(1/2)) * ((5,000 - 42) / (5,000 - 1))^(1/2)
= 1.6973 * 0.995890
= 1.69

d)
If the population size (N) = 500 then the standard error of the mean = (Standard deviation / n^(1/2)) * ((N - n) / (N - 1))^(1/2)
= (11 / 42^(1/2)) * ((500 - 42) / (500 - 1))^(1/2)
= 1.6973 * 0.958037406
= 1.63