Q1

Try defining (a) the distribution of sample means, (b) describe what the Central Limit Theorem tells us, (c) talk about the relationship between the mean of the sample means and the population mean for a given variable, and (d) define what the standard error of a population mean is, in concept. (No calculations in this problem).

1. Briefly define each of the following: a. Distribution of sample means b. Central limit theorem c. Expected value of M d. Standard error of M4. Under what circumstances is the distribution of sample means definitely a normal distribution?5. A random sample is selected from a population with a standard deviation of o = 18. a. On average, how much difference should there be between the sample mean and the population mean for a random sample of n = 4 scores from this population? b. On average, how much difference should there be for a sample of n = 9 scores? c. On average, how much difference should there be for a sample of n = 36 scores?9. A population forms a normal distribution with a mean of u = 85 and a standard deviation of o = 24. For each of the following samples, compute the z-score for the sample mean. a. M = 91 for n = 4 scores b. M = 91 for n = 9 scores c. M = 91 for n = 16 scores d. M = 91 for n = 36 scores7. For a population with a mean of u = 40 and a standard deviation of o = 8, find the z-score corresponding to each of the following samples. a. X = 34 for a sample of n = 1 score b. M = 34 for a sample of n = 4 scores c. M = 34 for a sample of n = 16 scores11. Scores from a questionnaire measuring social anxiety form a normal distribution with a mean of u = 50 and a standard deviation of o = 10. What is the probabil- ity of obtaining a sample mean greater than M = 53, a. for a random sample of n = 4 people? b. for a random sample of n = 16 people? c. for a random sample of n = 25 people?13. A population has a mean of u = 30 and a standard deviation of o = 8 a. If the population distribution is normal, what is the probability of obtaining a sample mean greater than M = 32 for a sample of n = 4? b. If the population distribution is positively skewed, what is the probability of obtaining a sample mean greater than M = 32 for a sample of n = 4? c. If the population distribution is normal, what is the probability of obtaining a sample mean greater than M = 32 for a sample of n = 64