Z-score Principles

Question 1

When would you use a z-score method?

Answer 1

When the given question includes the population standard deviation (i.e. the population standard deviation is known)

Question 2

Equation for the Standard deviation of samples:

Question 3

define inferential statistics.

Answer 3

Inferential statistics are used to make conclusions (inferences) about the population. They use sample parameters to make inferences about population parameters.

Question 4

Properties of Sampling Distribution of the Mean.

Answer 4

• keeps a normal distribution
• mean is “u” (meaning that M is an unbiased estimator of “u”)
• standard deviation (standard error of the mean) is σM =σ/√N

Question 5

Effect of n on σM

Answer 5

the larger the n, the more accurate the sample is, less σM

the larger the sample, the closer the mean is to the populations

Question 6

Effect of σ on σM

Answer 6

effect of population mean, less accurate population mean assumes less accurate sample mean

Question 7

Normal Distributions

Answer 7

• symmetrical, mean in centre
• 50% below and above mean

Question 8

Premise of Z-scores

Answer 8

expressing scores in terms of standard deviation

Question 9

Z-score Formula

Answer 9

Z = M - μ / σM

• can use to find area under the curve

Question 10

Confidence Intervals using Z-scores

Answer 10

μ upper = μ + (Zc x σM)

μ lower = μ - (Zc x σM)

Question 11

Point VS Interval Estimate of μ

Answer 11

The sample mean (M) is the best point of estimate for μ, because it is an unbiased estimator

Interval Estimates constructs ranges of a values which we believe, with a level of confidence, covers the true value

Question 12

Different Confidence Interval Rates

Answer 12

let α = error rate as a probability
α for 95% confidence, α =.05
α for 90% confidence, α =.10
α for 99% confidence, α =.01