Stats Exam #2

A population distribution has σ = 6. What position in this distribution is identified by a z-score of z = +2.00?

12 points above the mean

If the Z score is negative, Greater than is: lesser than is:

Column B Column C

In the unit distribution table if a z score is positive you look for greater than in: and lesser than in:

Column C Column B

In a distribution with σ = 20, a score that is below the mean by 10 points will have a z-score of z = 0.50.

False

Samples of n = 4 scores are selected from a population. If the distribution of sample means has a standard error σ = 5 points, then the population from which the samples were obtained has a standard deviation of σ = 20.

False

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

Sampling with replacement

Once an element has been included in the sample, it is returned to the population. A previously selected element can be selected again and therefore may appear in the sample more than once.

What is the expected value of M?

The Mean of the distribution of sample means

A positive z-score always corresponds to a score that is greater than the mean. ​

True

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

True

For a population with a mean of μ = 80, any score greater than 80 will have a positive z-score.

True

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

True

The proportion in the body of a normal distribution can never be less than 0.50.

True

The tail is on the right side of a normal distribution for any z-score value greater than zero.

True

Two samples probably will have different means even if they are both the same size and they are both selected from the same population.

True

Random Sample

a sample that fairly represents a population because each member has an equal chance of inclusion

Distribution of sample means

the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population

Population Variance

the smaller the variance in the population, the more probable it is that the sample mean will be close to the population mean