6- Sampling Distributions

A sample is obtained from a population with μ = 100 and σ = 20. Which of the following samples would produce the z-score closest to zero? a. A sample of n = 25 scores with M = 102 b. A sample of n = 100 scores with M = 102 c. A sample of n = 25 scores with M = 104 d. A sample of n = 100 scores with M = 104

a

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 sample means tend to form a normal-shaped distribution. b. The distribution of sample means will have the same shape as the sample distribution. c. The sample will 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

A sample of n = 4 scores has a standard error of 12. What is the standard deviation of the population from which the sample was obtained? a. 48 b. 24 c. 6 d. 3

b

For a sample selected from a normal population with μ = 100 and σ = 15, which of the following would be the most extreme and unrepresentative? a. M = 90 for a sample of n = 9 scores b. M = 90 for a sample of n = 25 scores c. M = 95 for a sample of n = 9 scores d. M = 95 for a sample of n = 25 scores

b

If all the possible random samples, each with n = 9 scores, are selected from a normal population with μ = 80 and σ = 18, and the mean is calculated for each sample, then what is the average value for all of the sample means? a. 9 b. 80 c. 9(80) = 720 d. Cannot be determined without additional information

b

If random samples each with n = 9 scores, are selected from a normal population with μ = 80 and σ = 18, and the mean is calculated for each sample, then how much distance is expected on average between M and μ? a. 2 points b. 6 points c. 18 points d. Cannot be determined without additional information

b

A random sample is selected from a population with μ = 80 and σ = 20. How large must the sample be to ensure a standard error of 2 points or less? a. n ≥ 10 b. n ≥ 25 c. n ≥ 100 d. It is impossible to obtain a standard error of less than 2 for any sized sample.

c

A random sample of n = 4 scores is obtained from a normal population with μ = 20 and σ = 4. What is the probability of obtaining a mean greater than M = 22 for this sample? a. 0.50 b. 1.00 c. 0.1587 d. 0.3085

c

A sample of n = 16 scores is obtained from a population with μ = 70 and σ = 20. If the sample mean is M = 75, then what is the z-score corresponding to the sample mean? a. z = 0.25 b. z = 0.50 c. z = 1.00 d. z = 2.00

c

For a normal population with μ = 80 and σ = 20, which of the following samples is least likely to be obtained? a. M = 88 for a sample of n = 4 b. M = 84 for a sample of n = 4 c. M = 88 for a sample of n = 25 d. M = 84 for a sample of n = 25

c

Which of the following would cause the standard error of M to get smaller? a. Increasing both the sample size and standard deviation b. Decreasing both the sample size and standard deviation c. Increasing the sample size and decreasing the standard deviation d. Decreasing the sample size and increasing the standard deviation

c

A random sample of n = 4 scores is obtained from a normal population with μ = 40 and σ = 6. What is the probability of obtaining a mean greater than M = 46 for this sample? a. 0.3085 b. 0.1587 c. 0.0668 d. 0.0228

d

A sample obtained from a population with σ = 10 has a standard error of 2 points. How many scores are in the sample? a. n = 5 b. n = 10 c. n = 20 d. n = 25

d

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 samples of size 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 mean and variance. b. The mean and the variance for n = 25 will both be larger than the mean and variance for n = 2. c. The mean and the variance for n = 25 will both be smaller than the mean and variance for n = 2. d. The variance for n = 25 will be smaller than the variance for n = 2 but the two distributions will have the same mean.

d

If random samples, each with n = 4 scores, are selected from a normal population with μ = 80 and σ = 10, then what is the expected value of the mean for the distribution of sample means? a. 2.5 b. 5 c. 40 d. 80

d