# 13 Probability Statements: True or False?

Based on Questions tell whether True or False

1. For any normal distribution exactly 97.50% of the z-score values are less than z=1.96.

2. For any normal distribution, the proportion located between the mean and z=1.40 is 0.9192.

3. When determining the probability of selecting a score that is below the mean, you will get a negative value for probability.

4. It is possible for the distribution of sample means to be normal even if it is based on samples with less than n=30.

5. If a sample of at least 30 scores is randomly selected from a normal population, the sample mean will be equal to the population mean.

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

7. If samples are selected from a normal population,the distribution of sample means will also be normal.

8. According to the central limit theorem, the expected value for a sample mean becomes smaller approaching zero, as the sample size approaches infinity.

9. According to the central limit theorem, the standard error for a sample mean becomes smaller approaching zero, as the sample size approaches infinity.

10. For a sample consisting of a single score (n=1), the standard error is equal to the population standard deviation.

11. Assuming that all other factors are held constant, as the population variability increases, the standard error will also increases.

12. If the standard deviation for a population increases, the standard error for sample means from the population will also increase.

13. The smallest possible standard error is obtained when a sample sample is taken from a population with a small standard deviation.

https://brainmass.com/statistics/probability/probability-statements-true-false-551733

## SOLUTION This solution is **FREE** courtesy of BrainMass!

1. For any normal distribution exactly 97.50% of the z-score values are less than z=1.96.

True as P(Z>1.96)=97.50%.

2. For any normal distribution, the proportion located between the mean and z=1.40 is 0.9192.

False as mean is unknown.

3. When determining the probability of selecting a score that is below the mean, you will get a negative value for probability.

False as probability can not be negative.

4. It is possible for the distribution of sample means to be normal even if it is based on samples with less than n=30.

False as distribution is based on samples with more than n=30.

5. If a sample of at least 30 scores is randomly selected from a normal population, the sample mean will be equal to the population mean.

False as there is no relation between normal mean and sample mean.

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

True as explained in question 4.

7. If samples are selected from a normal population,the distribution of sample means will also be normal.

False as only if n is larger than 30, we can assume that the distribution of sample means will also be normal.

8. According to the central limit theorem, the expected value for a sample mean becomes smaller approaching zero, as the sample size approaches infinity.

False as expected value for a sample mean remains the same as the sample size approaches infinity.

9. According to the central limit theorem, the standard error for a sample mean becomes smaller approaching zero, as the sample size approaches infinity.

True as standard error for a sample mean is inversely related to n.

10. For a sample consisting of a single score (n=1), the standard error is equal to the population standard deviation.

False as there is no relation between population standard deviation and standard deviation.

11. Assuming that all other factors are held constant, as the population variability increases, the standard error will also increases.

True.

12. If the standard deviation for a population increases, the standard error for sample means from the population will also increase.

False as there is no relation between population standard deviation and standard deviation.

13. The smallest possible standard error is obtained when a sample sample is taken from a population with a small standard deviation.

False as there is no relation between population standard deviation and standard deviation.

https://brainmass.com/statistics/probability/probability-statements-true-false-551733