Stat Chap. 7 Probability and Samples: The Distribution of Sample Means
Samples of size n = 9 are selected from a population with μ = 80 with σ = 18. What is the standard error for the distribution of sample means?
6
Central limit theorem
mathematical proposition which serves as a cornerstone for much of inferential statistics
Expected value of M
mean of the distribution of sample means which is always equal to the population mean
Standard error of M
measure of distance expected between sample mean and population mean
Sampling distribution
statistics obtained by selecting all possible samples of a specific size from a population
A random sample of n = 4 scores is obtained from a population with a mean of µ = 80 and a standard deviation of σ = 10. If the sample mean is M = 90, what is the z-score for the sample mean?
z = 2.00
For a population with µ = 80 and σ = 20, the distribution of sample means based on n = 16 will have an expected value of ____ and a standard error of ____.
80; 5
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 = 6 scores is selected from a population. Which of the following distributions will definitely be normal?
None of the distributions (the sample, population, or distribution of sample means) will definitely be normal.
A random sample of n = 60 scores is selected from a population. Which of the following distributions will definitely be normal?
The distribution of sample means will definitely form a normal distribution.
A sample of n = 4 scores is selected from a normal population with a mean of µ = 50 and a standard deviation of σ = 20. What is the probability of obtaining a sample mean greater than M = 48?
p = 0.5793
A random sample of n = 16 scores is selected from a normal distribution with μ = 500 and σ = 200. For this sample, which of the following is true?
p(402 < M < 598) = 0.95
What symbol is used to identify the standard error of M?
σM
Distribution of sample means
collection for all the possible random data sets of a particular size
On average, a sample of n = 16 scores from a population with σ = 10 will provide a better estimate of the population mean than you would get with a sample of n = 16 scores from a population with σ = 5.
false
Sampling distribution
group of statistics obtained by selecting all possible samples of a specific size
Samples of size n = 9 are selected from a population with μ = 80 with σ = 18. What is the expected value for the distribution of sample means?
80
A sample of n = 4 scores is selected from a normal population with μ = 30 and σ = 8. The probability of obtaining a sample mean greater than 34 is equal to the probability of obtaining a z-score greater than z = 2.00.
False
If a sample of n = 4 scores is obtained from a population with μ = 70 and σ = 12, what is the z-score corresponding to a sample mean of M = 73?
NOT z = 1.00
For a normal population with µ = 40 and σ = 10, which of the following samples has the highest probability of being obtained?
NOT M is less than 36 for a sample of n = 4
Sampling error
natural discrepancy between a statistic and its corresponding population parameter
law of large numbers
rule that larger sample size increases probability that sample and population means will be close
A sample is selected from a population with µ = 30 and σ = 10. If the sample mean of M = 34 corresponds to z = +2.00, then the sample size is n = 25.
true
A sample of n = 9 scores is selected from a normal population with a mean of µ = 80 and a standard deviation of σ = 12. The probability that the sample mean will be greater than M = 86 is equal to the probability of obtaining a z-score greater than z = 1.50
true
As the population standard deviation increases, the standard error will also increase.
true
If the sample size is equal to the population variance (n = σ2), then the standard error is equal to 1.
true
Samples of n = 16 are selected from a population. If the distribution of sample means has a standard error of 2 points, then the population has a standard deviation of σ = 8.
true
The mean for the distribution of sample means is always equal to the mean for the population from which the samples are obtained.
true