stats exam 1 pt.2 (variability, Z scores)

For a population with a standard deviation of σ = 10, what is the z-score corresponding to a score that is 5 points below the mean?

-.50

If an entire population with μ = 60 and σ = 8 is transformed into z-scores, then the distribution of z-scores will have a mean of _______ and a standard deviation of _______.

0;1

Standardising a distribution

1. Original raw scores transformed to z-scores. 2. The z-scores are transformed to new X values so that the specific predetermined μ and σ are attained.

In a population with a standard deviation of σ = 5, a score of X = 44 corresponds to a z-score of z = 2.00. What is the population mean?

34

For a population with μ = 80 and σ = 10, what is the X value corresponding to z = -2.00?

60

Which of the following is true for most distributions?

Around 70% of the scores will be located within one standard deviation of the mean.

For any distribution, what is the z-score corresponding to the median?

Cannot be determined from the information given

Under what circumstances is the computational formula preferred over the definitional formula when computing SS, the sum of the squared deviations, for a sample?

When the sample mean is not a whole number

A population with μ = 41 and σ = 4 is standardized to create a new distribution with μ = 50 and σ = 10. In this transformation, a score of X = 39 from the original distribution will be transformed into a score of X = 55. (T or F)

false

For a population with μ = 34, a score of X = 31 corresponds to z = -1.00. The standard deviation for the population is σ = 6. (T or F)

false

In a distribution with μ = 80 and σ = 20, a score of X = 95 corresponds to z = 1.50. (T or F)

false

A population of scores has m = 50 and s = 5. If every score in the population is multiplied by 3, then what are the new values for the mean and standard deviation?

m = 150 and s = 15

probability of A=

number of outcomes classified as A/total number of possible outcomes

A population with μ = 54 and σ = 12 is standardized to create a new distribution with μ = 100 and σ = 20. After the transformation, an individual receives a new score of X = 95. The original score for this individual was X = 51. (T or F)

true

A professor standardizes exam scores so that all exams have μ = 50 and σ = 10. If the original scores from the exam have μ = 42 and σ = 6, then a student with an original exam score of X = 45 would receive a standardized score of X = 55. (T or F)

true

A z-score of z = +1.00 always indicates a location exactly 1 standard deviation above the mean. (T or F)

true

For any distribution of scores, the location identified by z = +1 and the location identified by z = -1 are exactly the same distance from the mean. (T or F)

true

If an entire population of N = 20 scores is transformed into z-scores, the set of 20 z-scores will have ∑X = 0. (T or F)

true

In a sample with s = 6, a score of X = 53 corresponds to z = -0.50 The mean for this sample is M = 56. (T or F)

true

On an exam, Tom scored 12 points above the mean and had a z-score of +2.00. The standard deviation for the set of exam scores must be σ = 6. (T or F)

true

raw score

x= mean+(Z times Standard deviation)

equation for z score

z=(x-mean)/standard deviation