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

If a sample is selected from a normal population with µ=50 and σ=20, which of the following samples is extreme and very unlikely to be obtained?

a. M=45 for a sample of n=4 scores

b. M=45 for a sample of n=25 scores

c. M=45 for a sample for n=100 scores

d. The three samples are equally likely to be obtained

c. M=45 for a sample of n=100 scores

A random sample is obtained from a population with µ=80 and σ=10 and a treatment is administered to the sample. Which of the following outcomes would be considered noticeably different from a typical sample that did not receive the treatment?

a. n=25 with M=81

b. n=25 with M=83

c. n=100 with M=81

d. n=100 with M=83

d. n=100 with M=83

If a sample of n=25 scores is selected from a normal population with µ=80 and σ=10, then what sample means form the boundaries that separate the middle 95% of all sample means from the extreme 5% in the tails?

a. 76.08 and 83.92

b. 76.70 and 83.30

c. 77.44 and 82.56

d. 78 and 82

a. 76.08 and 83.92

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

a. It is always normal

b. Only if the population distribution is normal

c. Only if the sample size is greater than 30

d. If the population is normal or if the sample size is greater than 30

d. If the population is normal or if the sample size is greater than 30

A random sample of n=6 scores is selected from a population. Which of the following distributions will definitely be normal?

a. The scores in the sample will form a normal distribution

b. The scores in the population will form a normal distribution

c. The distribution of sample means will form a normal distribution

d. The sample, the population, and distribution of sample means definitely will not be normal

c. The distribution of sample means will form a normal distribution