### Distribution of Sample Means, Standard Deviation, Sample Size, Standard Error

The key term in these Statistic chapters include Distribution, Sample Means, Standard Deviation, Sample Size, Standard Error, Probability, Normal, Population, Random Samples, Normal Population, Z-Score, – Statistics

Under what circumstances will the distribution of sample means be normal?

**IF the POPULATION is normal or if the sample size is greater than 30.**

Samples of size n = 9 are selected from a population with u = 80 with o = 18. What is the standard error for the distribution of sample means?

**6**

What is the standard error of M?

**It is the STANDARD deviation of the distribution of sample means.**

A sample of N = 4 scores is selected from a population with u = 40 with o = 8, and the sample mean is M = 43. What

is the expected value for the sample mean?

**40**

A sample of n = 9 scores is obtained from a population with u = 70 and o = 18. If the sample mean is M = 76, what is the z-score for the sample mean?

**z = 1.00**

If random samples, each with n = 9 scores, are selected from a normal population with u = 80 and o = 36, what is the standard error for the distribution of sample means?

**6 points**

For the population with u = 80 and o = 6, what is the Z – SCORE corresponding to X = 68?

**– 2.00**

For a population with u = 40 and o = 8, what is the X value corresponding to z = 1.50?

**52**

A population has u = 50. What value of 0 would make X = 55 a central, representative score in the population?

**o = 10**

A sample obtained from a population with o = 12 has a standard error of 2 points. How many scores are in the sample?

**n = 6**

A random sample of n = 16 scores is obtained from a population with o = 12. If the sample mean is 6 points greater than the population mean, what is the z-score for the sample mean?

**+2.00**

What is the standard error of M?

**It is the STANDARD deviation of the distribution of sample means.**

Under what circumstances will the distribution of sample means be normal?

**IF the POPULATION is normal or if the sample size is greater than 30.**

A random sample of n = 9 scores is obtained from a normal population with u = 40 and o = 18. What is the probability that the sample meean will be greater than M = 43.

**0.3085**

A sample of n = 4 scores is selected from a normal population with a mean of u = 50 and a standard deviation of 0 = 20. What is the probability of obtaining a sample mean greater than M = 48.

**p = 0.5793**

Which of the following Z- SCORE values represents the location farthest from the mean?

**z = -2.00**

A population of scores has u = 80. In this population, a score of X = 86 corresponds to z = +2.00. What is the population standard deviation?

**3**

Which combination of factors will produce the largest value for the standard error?

**A small sample and a large standard deviation**

Under what circumstances will the distribution of sample means be normal?

**IF the POPULATION is normal or if the sample size is greater than 30.**

What is the standard error of M?

**It is the STANDARD deviation of the distribution of sample means.**

For the population with u = 80 and o = 6, what is the Z-SCORE corresponding to X = 68?

**– 2.00**

For a population with u = 40 and o = 8, what is the X value corresponding to z = 1.50?

**52**

A population has u = 50. What value of 0 would make X = 55 a central, representative score in the population?

**o = 10**

A sample obtained from a population with o = 12 has a standard error of 2 points. How many scores are in the sample?

**n = 6**