PSY 207 Exam 2 copy
What does the normal distribution look like when there is a higher standard deviation?
"Flatter" distribution
What is a Null Hypothesis (H0)?
"No difference"
What does the normal distribution look like when there is a lower standard deviation?
"Skinnier" distribution
What are the steps to Hypothesis Testing?
1. State hypothesis 2. Determine the "critical region" for decision criteria. 3. Compute a test statistics. 4. Make Decision
What are the Properties of the Sampling Distribution of the Mean?
1. The Mean, µM = µ 2. The Standard Error, σM = σ/√n 2. Sample Size and Standard Error 4. Central Limit Theorem
Calculate the Z-Score µ = 27, X = 32, σ = 4
1.25
Calculate the Standard Error: σ = 12.7, n = 40
2.01
Calculate the Standard Error: σ = 12, n = 27
2.31
Calculate σ µ = 5, z-score = 0.77, X = 7
2.6
Calculate the Standard Error: σ = 33, n = 145
2.74
Calculate X µ = 44, z-score = 2.5, σ = 3
51.5
What is the "Body?"
Big region, "typical"
If you choose a larger alpha (a)
Critical region gets larger.
If you choose a smaller alpha (a)
Critical region gets smaller.
Two-Tailed Test
Determine a difference between two groups of data.
Frequencies are Probabilities
Distribution = expectation based on H0 Critical Region is Extreme(s)
True or False: Probability can be negative
False!
State the H0 Hypothesis for the scenario below: A PAL decided to conduct an experiment to determine if attending PAL sessions increases the exam grades of the students who attend on a weekly basis. Sample Size: 10 Alpha Level (a): 0.05
PAL sessions do not have any effect on students exam results and are not higher.
One-Tailed Test
Predict specific direction.
What is the y-axis of a Probability Density Curve
Probability
Hypothesized Sampling Mean
Sampling distribution we used to make decisions about the null hypothesis.
What is the "Tail?"
Small region, "extreme"
State the H1 Hypothesis for the scenario below: A PAL decided to conduct an experiment to determine if attending PAL sessions increases the exam grades of the students who attend on a weekly basis. Sample Size: 10 Alpha Level (a): 0.05
Students who attend weekly PAL sessions get exam results that are higher
If µ ≠ µM...
The Null Hypothesis is FALSE
If µ = µM...
The Null Hypothesis is TRUE
What is the table called that we use to find probability values?
The Unit Normal Table
What is the relationship between sample size and standard error?
The larger the sample size, the smaller the standard error of the mean. Inverse relationship.
What is the Central Limit Theorem?
The larger the size of each sample, the sampling distribution of the mean will better approximate the normal curve.
What is the Law of Large Numbers?
The larger the size of the sample taken from the population, the closer the sample mean will be to the population mean.
Alternative Hypothesis (H1)
The population of interest is different than the general population.
What does it mean that the null hypothesis is false?
There is evidence.
What does it mean that the null hypothesis is true?
There is no evidence
What is the x-axis of a Probability Density Curve
Variable
What is the equation for a Z-Test
Z = (M - µM)/σM
What is a problem with inferential statistics?
we will almost never actually know the actual mean and standard deviation of a population.
Probability Density Curve
when you plot a smooth curve rather than a histogram or frequency polygon.
How do you calculate a z-score?
z = (X-µ)/σ
Relative Frequency Equation
p(x) = f(X)/N
Calculate the Z-Score µ = 10, X = 8, σ = 2
-1
What is the range of variability?
0 - 1
Calculate the Probability: A population of scores... µ = 23.00 σ = 5.88 Above X = 27
0.2483
Calculate the Probability: A population of scores... µ = 145.00 σ = 16.5 Below X: 134
0.2514
Calculate the Probability: A population of scores... µ = 145.00 σ = 16.5 Above X = 155
0.2709
Calculate the Probability: A population of scores... µ = 145.00 σ = 16.5 In Between: X: 155 X: 133
0.4930
Calculate Probability of Cups: µ = 6, σ = 2 What is the probability that the mean of 7 cups will be between 6.5 and 4.7?
0.7027
Calculate the Probability: A population of scores... µ = 23.00 σ = 5.88 In Between: X: 33 X: 17
0.8015
Calculate the Probability: A population of scores... µ = 23.00 σ = 5.88 Above X = 17
0.8461
Does Z corresponding to the M fall in critical region?
Not More Extreme: H0 is confirmed/retained More Extreme: H0 is disconfirmed and you have statistical significance.
Stating Hypothesis For Two-Tailed Test
H0: M = µ H1: M ≠ µ
Stating Hypothesis For One-Tailed Test, Positive
H0: M ≤ µ H1: M > µ
Stating Hypothesis For One-Tailed Test, Negative
H0: M ≥ µ H1: M < µ
What happens to variability with an increasing n?
It shrinks!
What does the z-score tell us when we convert from raw score to z-score?
It tells us the magnitude of deviation or distance of a raw score from the mean. The sign tells us the position of the score relative to the mean.
According to the Central Limit Theorem, what the shape of a distribution look like with small samples?
Less normal
How are inferential statistics used?
Make use of probabilities to test hypotheses about populations based on samples.
According to the Central Limit Theorem, what the shape of a distribution look like with large samples?
More normal
What is a 5% criterion called?
alpha (a)
Postive Z-Score
corresponds to raw scores above the mean.
Negative Z-Score
corresponds to raw scores below the mean.
What is the symbol for Mean Sampling Distribution (Expected Value)?
µM
What is the symbol for Standard Deviation Sampling Distribution (Standard Error)?
σM
What is the equation for Standard Error?
σM = σ/(√n)
How else can the equation for σM look?
√(σ^2/n)
