Ch. 7 Quiz 7 (PSYC 2013, NWACC)

Q: A random sample of n = 16 scores is obtained from a population with s = 12. If the sample mean is 6 points greater than the population mean, what is the z-score for the sample mean?

+2.00

Q: A random sample of n = 4 scores is obtained from a normal population with m = 30 and s = 8. What is the probability that the sample mean will be smaller than M = 22?

0.0228

Q: A sample of n = 4 scores is selected from a population with m = 50 and s = 12. If the sample mean is M = 56, what is the z-score for this sample mean?

1.00

Q: A sample of n = 16 scores has a standard error of 4. What is the standard deviation of the population from which the sample was obtained?

16

Q: If random samples, each with n = 4 scores, are selected from a normal population with m = 80 and s = 36, what is the standard error for the distribution of sample means?

18

Q: For a particular population, a sample of n = 4 scores has a standard error of 6. For the same population, a sample of n = 16 scores would have a standard error of _____.

3

Q: A sample is selected from a population with m = 50 and s = 12. If the sample mean of M = 56 produces a z-score of z = +1.00, then how many scores are in the sample?

4

Q: A sample of n = 4 scores is selected from a population with m = 40 with s = 8, and the sample mean is M = 43. What is the standard error for the sample mean?

4

Q: A sample of n = 4 scores is selected from a population with m = 40 with s = 8, and the sample mean is M = 43. What is the expected value for the sample mean?

40

Q: A sample of n = 16 scores is selected from a population with m = 80 with s = 20. On average, how much error would be expected between the sample mean and the population mean?

5 points

Q: If random samples, each with n = 9 scores, are selected from a normal population with m = 80 and s = 18, how much difference, on average, should there be between a sample mean and the population mean?

6 points

Q: A sample is obtained from a population with m = 100 and s = 20. Which of the following samples would produce the most extreme z-score?

A sample of n = 100 scores with M = 104

Q: Which combination of factors will produce the largest value for the standard error?

A small sample and a large standard deviation

T/F: A population has m = 60 and s = 30. For a sample of n = 25 scores from this population, a sample mean of M = 55 would be considered an extreme value.

False

T/F: A sample is obtained from a population with s = 20. If the sample mean has a standard error of 5 points, then the sample size is n = 4.

False

T/F: A sample of n = 25 scores is selected from a population with m = 50 and s = 10. The probability of obtaining a sample mean greater than 55 is p = 0.3085.

False

T/F: A sample of n = 4 scores is selected from a normal population with m = 30 and s = 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

T/F: A sample of n = 9 scores is selected from a population with m = 40 and s = 18. If the sample mean corresponds to z = -1.00, then the sample mean is M = 31.

False

T/F: If the sample size is doubled, the standard error will be cut in half.

False

T/F: If the sample size is equal to the population standard deviation (n = s), then the standard error for the sample mean is equal to 1.00.

False

T/F: If the sample size is increased, then the standard error for sample means will also increase.

False

T/F: In order for the distribution of sample means to be normal, it must be based on samples of at least n = 30 scores.

False

T/F: On average, a sample of n = 16 scores from a population with s = 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 s = 5.

False

T/F: The mean for a sample of n = 9 scores has a standard error of 2 points. This sample was selected from a population with a standard deviation of s = 18.

False

Q: 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

Q: What happens to the standard error of M as sample size increases?

It decreases

Q: What is the expected value of M?

It is the mean of the distribution of sample means.

Q: What is the standard error of M?

It is the standard deviation of the distribution of sample means.

Q: What happens to the expected value of M as sample size increases?

It stays constant.

Q: A sample is selected from a normal population with m = 50 and s = 12. Which of the following samples would be considered extreme and unrepresentative for this population?

M = 56 and n = 16

Q: A sample of n = 4 scores is obtained from a population with m = 70 and s = 8. If the sample mean corresponds to a z-score of 2.00, what is the value of the sample mean?

M = 78

Q: A random sample of n = 60 scores is selected from a population. Which of the following distributions definitely will be normal?

The distribution of sample means will form a normal distribution.

T/F: A researcher obtained M = 27 for a sample of n = 36 scores selected from a population with m = 30 and s = 18. This sample mean corresponds to a z-score of z = -1.00.

True

T/F: A sample is selected from a population with m = 30 and s = 10. If the sample mean of M = 34 corresponds to z = +2.00, then the sample size is n = 25.

True

T/F: A sample of n = 16 scores is selected from a population with m = 70 and s = 8. It is very unlikely that the sample mean will be greater than 78.

True

T/F: A sample of n = 9 scores is selected from a normal population with a mean of m = 80 and a standard deviation of s = 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

T/F: A sample of n = 9 scores is selected from a population with m = 50 and s = 12. The probability of obtaining a sample mean greater than 46 is p = 0.8413.

True

T/F: According to the central limit theorem, the standard error for a sample mean becomes smaller as the sample size increases.

True

T/F: If samples are selected from a normal population, the distribution of sample means will also be normal.

True

T/F: If the sample size is equal to the population variance (n = s2), then the standard error is equal to 1.

True

T/F: On average, a sample of n = 16 scores will provide a better estimate of the population mean than you would get with a sample of n = 9 scores from the same population.

True

T/F: Samples of n = 9 scores are selected from a population. If the distribution of sample means has an expected value of 40, then the population has a mean of m = 40.

True

T/F: The mean for the distribution of sample means is always equal to the mean for the population from which the samples are obtained.

True

Q: A sample from a population with m = 40 and s = 8 has a mean of M = 36. If the sample mean corresponds to a z = -1.00, then how many scores are in the sample?

n = 4

Q: A sample of n = 4 scores is selected from a normal population with a mean of m = 50 and a standard deviation of s = 20. What is the probability of obtaining a sample mean greater than M = 48?

p = 0.5793

Q: What symbol is used to identify the standard error of M?

sM

Q: A sample of n = 16 scores is obtained from a population with m = 50 and s = 16. If the sample mean is M = 54, then what is the z-score for the sample mean?

z = 1.00