Chapter 8: Hypothesis Testing
Research Question:
Does a “college motivational” seminar influence college students’
attitudes about college?
Survey of Study Habits & Attitudes (0 – 200; less - more favorable)
Known population parameters:
 = 115
 = 30
A sample (n = 100) of college students is put through the program:
X = 126
Did the intervention change attitudes?
Chapter 8: Page 1
Attitudes do seem improved—the mean value from the sample is larger
than the known population average
Remember: SAMPLES VARY! Could this apparent improvement just be
due to chance?
How can we tell?
Hypothesis Testing:
 “Process by which decisions are made concerning the values of parameters”
 In this case, compare X to known 
 Differences between X and  expected simply on the basis of chance
sampling error
 How do we know if it’s just chance?
Sampling distributions!
Chapter 8: Page 2
College Motivational Seminar: does it change attitudes?
Known population:  = 115
 = 30
 Assume seminar does NOT affect attitudes
 Sample mean ( X = 126) should be close to  if assumption is true
Known
population
mean: 115
100
105
Sample mean:
126
110
115 120 125 130
Chapter 8: Page 3
Setting up the Hypotheses:
It is easier to prove that something is false, than that something is true
Assume opposite of what you believe. . .
And then find evidence that assumption is wrong!
Two mutually exclusive & competing hypotheses:
1. The “null” hypothesis (H0)
The one you assume is true
The one you hope to discredit
Assumes there is NO difference b/n the sample & popl’n values
2. The “alternative” hypothesis (H1)
The one you think or hope is true
Assumes there IS some difference b/n the sample & popl’n values
Chapter 8: Page 4
Form of H0 and H1 for one-sample mean:
H0:  = 115
H1:   115
 Hypotheses are always about population parameters, not sample statistics
H0:  = population value
H1:   population value
 This hypothesis is a non-directional (two-tailed) hypothesis
 Null hypothesis: No effect
 Alternative hypothesis: Some effect (doesn’t specify an increase or
decrease)
Chapter 8: Page 5
Criterion for rejecting H0: Creating a Decision Rule:
Will compute a test statistic (types vary based on data, design & question)
Then decide if the value of the test statistic is “improbable” under H0
Traditionally, a test statistic is considered “unlikely” if it is expected to occur:
 5 in a 100: has a probability of .05 or less (p  0.05)
 Look in tails of sampling distribution for the unlikely outcomes
 Divide distribution into two parts:
Values that are likely if H0 is true Values that are very unlikely if H0 is true
Values close to H0
Values far from H0
Values in the middle
Values in the tails
Chapter 8: Page 6
Selecting a “significance level”: 
Probability chosen as criteria for “unlikely”
Common convention:  = .05 (5%)
May set a smaller  to be more conservative ( p  0.01, 0.001)
Critical
Value
Unlikely
outcomes:
p = 0.025
Critical
Value
Unlikely
outcomes:
p = 0.025
Critical value(s) = boundary(ies) b/n likely & unlikely outcomes
Rejection region = area(s) beyond critical value(s); outcomes that lead to a
rejection of H0
Chapter 8: Page 7
Decision rule:
Reject H0 when observed test-statistic equals or exceeds Critical value
…when statistic falls in the rejection region
Otherwise, Fail to Reject (Retain) H0
Chapter 8: Page 8
Collect data and Calculate “observed” test statistic:
z-test for one sample mean:
z
X
X
z = sample mean – hypothesized population 
standard error
z
=
observed difference
difference due to chance
Don’t forget to compute standard error first!

X =
n
Chapter 8: Page 9
Compare Test Statistic to Critical Values:
 Does observed z equal or exceed CV?
(Does it fall in the rejection region?)
 If YES,
Reject H0 = “statistically significant” finding
 If NO,
Fail to Reject H0 = “non-significant” finding
Chapter 8: Page 10
Interpret results:
 Return to research question
 statistical significance = not likely to be due to chance
 Never “prove” H0 or H1
Chapter 8: Page 11
(1) Does the “college motivation seminar” influence attitudes about college?
Population:
 = 115  = 30
(2) Statistical Hypotheses:
H0:  = 115
H1:   115
(3) Decide on :
 = .05
(4) Critical values:
See Table E. 10 for Z scores
Chapter 8: Page 12
(5) Calculate test statistic:
n = 100
X = 126
Compute z-statistic:
z=
z=
X
x
X = 
z=
n
126 115
x
 X = 30
100
126 115
 3.67
3
(6) compare test statistic to critical values:
z = 3.67
Critical values of Z (.05) = 1.96
Obtained Z exceeds critical value
Chapter 8: Page 13
(7) Interpret results:
Seminar appears to improve attitudes. Difference not likely due to chance.
“The college motivational seminar appears to have improved the attitudes of those
who attended, z = 3.67, p  .05, two-tailed.”
Italicize the test statistic
used and the “p” in the
p-value in type-written
reports
Underline the test
statistic used and the
“p” in the p-value in
hand-written reports
“The college motivational seminar appears to have improved the attitudes of those
who attended, z = 3.67, p  .05, two-tailed.”
Chapter 8: Page 14
Summary of Statistical Hypothesis Testing:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Formulate a research question
Formulate a research/alternative hypothesis
Formulate the null hypothesis
Collect data
Reference a sampling distribution of the particular statistic assuming that H0
is true (in the cases so far, a sampling distribution of the mean)
Decide on a significance level (), typically .05
Identify the critical value(s)
Compute the appropriate test statistic
Compare the test statistic to the critical value(s)
Reject H0 if the test statistic is equal to or exceeds the critical value, retain
otherwise
Chapter 8: Page 15