Chapter 7: The Distribution of Sample Means

If all the possible random sample of size n=5 are selected from a population with μ=50 and σ=10 and the mean is computed for each sample, then what value will be obtained for the mean of all the sample means?

a. 50

b. 50/5=10

c. 50(5)=2500

d. Around 50 but probably not equal to 50

a. 50

All the possible random samples of size n=2 are selected from a population with μ=40 and σ=10 and the mean is computed for each sample. Then all the possible sample of n=25 are selected from the same population and the mean is computed for each sample. How will the distribution of sample means for n=2 compare with the distribution for n=25?

a. The two distributions will have the same variances

b. The variance for n=25 will be larger than the variance for n=2

c. The variance for n=25 will be smaller than the variance for n=2

d. The variance for n=25 will be two times larger than the variance for n=2

c. The variance for n=25 will be smaller than the variance for n=2

If all the possible random samples of size n=25 are selected from a population with μ=80 and σ=10 and the mean is computed for each sample, then what shape is expected for the distribution of sample means?

a. The same means tend to form a normal-shaped distribution whether the population is normal or not

b. The sample means tend to form a normal distribution only if the population distribution is normal

c. The sample means tend to be distributed evenly across the scale, forming a rectangular-shaped distribution

d. There are thousands of possible samples and it is impossible to predict the shape of the distribution

a. The sample means tend to form a normal-shaped distribution whether the population is normal or not

If samples are selected from a population with μ=80 and σ=12, then which of the following samples will have the largest expected value for M?

a. n=10 scores with M=82

b. n=20 scores with M=84

c. n=30 scores with M=86

d. All of the samples will have the same expected value

d. All of the samples will have the same expected value

If random samples, each with n=4 scores, are selected from a population with µ=80 and σ=12, then how much distance is expected on average between the sample means and the population mean?

a. 4(12)=48 points

b. 12 points

c. 12/4=3 points

d. 12/√4=6 points

d. 12/√4=6 points

The standard distance between a sample mean and the population mean is 6 points for samples of n=16 scores selected from a population with a mean of μ=50. What is the standard deviation for the population?

a. 48

b. 24

c. 6

d. 3

b. 24

A normal population has µ=50 and σ=8. A random sample of n=16 scores from this population has a mean of 54. What is the z-score for this sample mean?

a. +0.50

b. +1.00

c. +2.00

d. +4.00

c. +2.00

A random sample of n=9 scores is obtained from a population with µ=50 and σ=9. If the sample mean is M=53, what is the z-score corresponding to the sample mean?

a. z=0.33

b. z=1.00

c. z=3.00

d. cannot determine without additional information

b. z=1.00

A random sample of n=25 scores is selected from a normally distributed population with μ=500 and σ=100. What is the probability that the sample mean will be less than 490?

a. 0.4602

b. 0.3085

c. 0.1587

d. 0.0062

b. 0.3085

For samples selected from a population with µ=100 and σ=15, which of the following has the smallest standard error?

a. a sample of n=4 scores

b. a sample of n=16 scores

c. a sample of n=25 scores

d. The three samples all have the same standard error

c. a sample of n=25 scores

For samples selected from a population with µ=40 and σ=20, what sample size is necessary to make the standard distance between the sample mean and the population mean equal to 2 points?

a. n=2

b. n=10

c. n=25

d. n=100

d. n=100

For a particular population, the standard distance between a sample mean and the population mean is 5 points for samples of n=4 scores. What would the standard distance be for samples of n=16 scores?

a. 5 points

b. 4 points

c. 2.5 points

d. 1 point

c. 2.5 points