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