Unit Three: Null Hypothesis Statistical Testing
Chapter 4.4: Probability & Normal Distribution
1. Determining % of scores that fall above or below a certain z score in a normal distribution:
Turn the raw
score into a zscore
•
𝑟𝑎𝑤− 𝜇
𝜎
Interest in the
proportion above or
below the mean?
• Depends on whether the
question is asking you for
something above or below.
Base it off of question
wording.
=Z
State the % that fall above/below
the mean using the table.
Draw
histogram and
shade area of
interest.
•Choose correct value in your book & look
up bsolute value.
2. Random sample, is it true? Why?
Random sample
Every case in a
population has an =
chance of selection.
Occurs everytime
you make a
selection.
a) Selecting people with the highest test scores.
 Not a random bc chance isn’t equal.
b) DPU students interested in going to grad school. Randomly
pick 30/50.
 No because people volunteer, then you choose – since
not everyone sees the ad, they don’t know about it
and therefore don’t have an equal chance.
c) Random digit dialing of homes with phones.
 Yes, all numbers have an = chance of being dialed.
3. Application of the law of large numbers to evaluate what scenario is more likely, given known probabilities.
For each event, determine the probability of the
outcome for option A & for B
Event(s)
•# of outcomes qualified as A/total # of outcomes.
• probabilities = more accurate w/ random sample.
The more events completed,
the closer you will be to the
true probabilities.
• Larger = closer accuracy.
Chapter 5: Probability & Normal Distribution and how they allow us to make inferences
about populations based on samples
1. Define the following…
Term/concept
Definition
Sampling Distribution Frequency distribution generated by taking repeated, random samples from a
population and generating some value, like a mean, for each sample.
 Behaves on simulations & math – not actually something you do in the study.
Dist. Of sample o Distribution of means taken from possible random samples of a certain size from
means
a population.
o Demostrates how much sampeling error exists in the samples.
 Tells the f of different means of the samples that will occur when taking all
samples of a certain size from a sample.
Standard Error o The Standard deviation of a sampling distribution of the mean.
 on average, how far each random sample mean is from the true population
mean.
2. Identify factors that affect the standard error & how they affect it.
Population Standard deviation
Sample Size
=
=
Standard error sample mean (i.e. its further from the population value).
Standard error sample mean (i.e. closer to true value so, more accurate).
3. What is the Central limit theorem? What does it tell us about the distribution of sample means?
Central Limit Theorem
Definition: 

3 predictions about sampling
distribution of the mean
What does it tell us about the
distribution of sample
means?
Statement about the shape that a sampling distribution of the mean
takes if the size of the sample is large and every possible sample were
obtained.
If we know the population, the mean, the standard deviation, & the
sample size, we can predict the behavior of sampling distribution of
means.
1. Mean of the distribution of sample means = true population value
2. Standard error of the distribution of the mean = the standard
deviation of the distribution of sample means.
3. Regardless of the shape of the original distribution, of scores, if you
take a large enough sample, distribution of samples will be normally
distributed.
a. Only applies to samples of 30+
1. It can predict the behavior of the sampling distribution means.
2. If sample is 30+, the shape will be a normal distribution.
Chapter 6: Null hypothesis testing and the logic of inferential statistics
Concept:
Definition
Hypothesis 


Null/Alternative 
Hypothesis 
One-tailed test 
Directional

Two-tailed test 
Non-directional

Alpha (or alpha 
level)


Critical Value 
P-value 

A proposed explanation for observed facts.
Statement OR prediction about a population
value.
Statement about population, not a sample.
They must cover all possible outcomes.
They must be all-inclusive/mutually exclusive.
1. Null (H0):
 Negative
 The population of the
explanatory variable  impact
on the outcome variable.
 Specific prediction
2. Alternative (H1):
 Positive
 Explanatory effects the
outcome in the population.
 Usually statement of what
researcher believes to be true
Predicts that explanatory has an impact on the
outcome variable in a SPECIFIC DIRECTION.
Says explanatory has positive or negative
affect.
Hypothesis predicting the explanatory variable
has an impact on the outcome variable, but
DOESN’T PREDICT DIRECTION.
Doesn’t say whether explanatory has positive
or negative affect.
probability that a result will fall in the rare
zone.
Null true = reject null
Set at .05 or 50%
Value of test stat that forms the boundary btw
the rare zone and the common zone of the
sampling distribution of the test statistic.
Probability of type I error:
 Error that occurs when the null is true
but rejected.
The same as alpha or significance level.
Example
Researcher is testing a technique
to improve intelligence…
1. (H0): “The technique does not
improve intelligence.”
a. Since it makes a
specific prediction, it
would say, “the
technique has 0
impact and doesn’t
improve intelligence
at all.
2. (H1): “The technique has
some impact on intelligence”
a. No specific prediction.
“Cardiac patients who receive
support from former patients
have less anxiety and higher
efficiency than other patients.”
“There is a difference in anxiety
and self-efficiency btw cardiac
patients who receive support
from former patients and those
who do not.”
2. Given the results, determine the outcome of hypothesis test.
3. Interpret…
4. Appropriate vs. inappropriate interpretations of the results of hypothesis test. Explain.
Day 13: get chapter/title (example of z-test is on page 195)
1. Z-Tests
Z Test
𝒛=
𝑴−𝝁
𝝈𝒎
Definition/Application
- Compares a sample mean to a population mean.
- Standard deviation of the population is known.
M = Sample mean
𝛍 = 𝐏𝐨𝐩 𝐦𝐞𝐚𝐧
𝛔𝐦
= 𝐬𝐭𝐝. 𝐞𝐫. 𝐦𝐞𝐚𝐧
Example
“The test used to see
whether adopted children
differ in intelligence from
the general population.”
2. Rejecting the Null or Failing to reject the Null
Decision
Appropriateness
Reject the Null  Z  1.96
 -1.96  Z
 Z = - 1.96 or 1.96
Fail to Reject the Null 
-1.96 < Z < 1.96
Interpretation
Results fall in rare zone so, the
doctor rejects the null – therefore,
he accepts the alternative and
concludes that the population
mean is something other than
100.