Chapters 9&10

Question 1

The Problem with Z-Scores

Answer 1

• requires more information than is usually available
• requires that we know the population standard deviation (σ)
• solution is to use the sample standard deviation

Question 2

Sample Standard Deviation Equation

Answer 2

s = square root of SS/df

Question 3

Standard Error Equation

Answer 3

σM = σ/square root of n

Question 4

Estimated Standard Error

Answer 4

Sm = s/square root of n

• SM is used to estimate the real standard error σM when the population standard deviation σ is unknown

Question 5

The t Statistic

Answer 5

z = M - µ / σm -> t = M - µ / Sm
• the t statistic is used to test hypotheses about the population mean µ when the value of σ is unknown
• the z distribution approximates a normal distribution as the sample size increases
• the t distribution approximates a normal distribution as the degrees of freedom (df) increase
- df = (n-1)

Question 6

Degrees of Freedom

Answer 6

degrees of freedom = df = n - 1
• df describes the number of scores in a sample that are independent and free to vary.
• because the sample mean places a restriction on the value of one score in the sample, there are (n – 1) degrees of freedom for the sample

Question 7

Shape of the t Distribution

Answer 7

• t-distribution has more variability than the normal z-distribution
- sample variability (s) changes for every sample
• as df increases, the t-distribution becomes a normal distribution

Question 8

Measuring the Effect Size for the t Statistic

Answer 8

• Cohen’s d = mean difference / standard deviation = M - µ / σ
• estimated d = mean difference / sample standard deviation = M - µ / s

Question 9

Magnitude of d

Answer 9

d = 0.2    small effect
d = 0.5    medium effect
d = 0.8    large effect