1. For a population with a standard deviation of = 20, how large a sample is necessary to have a standard error that is: a. less than or equal to 10 point? b. less than or equal to 4 points? c. less than or equal to 2 point? 2. The following samples were obtained from a population with a mean of = 40 and a standard deviation of = 8. Find the z-score corresponding to each sample mean. a. A sample of n = 4 scores with M = 38 b. A sample of n = 16 scores with M = 38 c. A sample of n = 64 scores with M = 38 3. Jumbo shrimp are those that require 10 to 15 shrimp to make a pound. Suppose that the number of jumbo shrimp in a 1-pound bag averages = 12.5 with a standard deviation of s=1, and forms a normal distribution. What is the probability of randomly picking a sample on n=25 1-pound bags that average more than M=13 shrimp per bag? 4. A population forms a normal distribution with a mean of = 75 and a standard deviation of = 20. a. What proportion of the sample means for n = 25 have values less than 80? In other words, find p(M < 80) for n = 25. b. What proportion of the sample means for n = 100 have values greater than 79? In other words, find p(M > 79) for n = 100. 5. For a normal-shaped distribution with = 50 and = 8: a. What proportion of the scores has values between 46 and 54? b. For samples of n = 4, what proportion of the sample mean have values between 46 and 54? c. For samples of n = 16, what proportion of the sample mean have values between 46 and 54? 6. A sample of n = 16 individuals is selected from a population with a mean of = 78. A treatment is administered to the individuals in the sample and, after treatment, the sample variance is found to be s2 = 144. a. If the treatment has a 4-point effect and produces a sample mean of M = 82, is this sufficient to conclude that there is a significant treatment effect using a two-tailed test with = .05 b. If the treatment has an 8-point effect and produces a sample mean of M = 86, is this sufficient to conclude that there is a significant treatment effect using a two-tailed test with = .05