exam 2 review

T/F: a negative z score will convert into a raw score that is above the mean of its distribution

False, A negative z score will convert into a raw score (X) that is below the population mean (μ).

what percentage of scores is 2 standard deviations or more below the mean?

2%

T/F: the standard deviation of the z distribution is 1.0

True, The mean of the standard normal (z) distribution is 0 and the standard deviation is 1.

what percentage of scores falls under the normal curve?

100%

what percentage of scores falls between 1 standard deviation below the mean and two standard deviations above the mean?

34% + 34% + 14% = 82%

what percentage of scores is within one standard deviation of the mean (above and below)?

34% + 34% = 68%

what percentage of scores lies between the mean and 2 standard deviations above the mean?

34% +14% = 48%

what percentage of scores is at least 1 standard deviation above the mean?

14% + 2% = 16%

what percentage of scores falls below the mean?

2% + 14% + 34% =50%

T/F: One implication of the central limit theorem is that a distribution of means will be less variable than a distribution of scores taken from the same population.

true, The standard error (σெ) is always smaller than the standard deviation of scores (σ) from the same population, so a distribution of means will always be narrower than a distribution of scores from the same population.

As the sample size (N) increases, the standard error....

Decreases - You can see this in the formula for calculating the standard error. As sample size (N) increases, the denominator of the formula gets large. If we divide the same standard deviation by a larger value, it will be smaller.

T/F: a z score allows one to compare scores to each other, but not when they are based on different scales

False, The purpose of standardization is to put variables from different populations (with different means and standard deviations) on a common scale in order to make meaningful comparisons..

T/F: When attempting to create a distribution of means, we sample with replacement; that is, we put data back in the sample after we have computed the mean of those data.

True, If we do this many, many times, the resulting distribution of means will be normally distributed with a mean of μM and a standard deviation of σெ. The standard deviation of the distribution of the sample mean is called the standard error to distinguish it from the standard deviation of the scores.

T/F: A distribution of means is comprised of many, many means of samples, all of the same size.

True, We divide by the square root of the sample size when computing the standard error because we would expect a distribution of means based on larger sample to vary less than a distribution of means based on a smaller sample.

T/F:Standard error is the variance of a distribution of means.

false, It is the standard deviation of a distribution of means (the square root of the variance).