PDF P-Value Approach to Hypothesis Testing G. Battaly
PValue Approach to Hypothesis Testing G. Battaly
April 01, 2019
9.2 & 9.3 Critical Value vs Pvalue Approach
GOALS: 1. Understand that 2 approaches of hypothesis testing exist: classical or critical value, and pvalue. We will use the pvalue approach. 2. Understand the critical value for the classical approach is the same z/2 or t/2 used in finding Confidence Intervals. 3. Learn the pvalue as the observed significance obtained from the data. 4. Find the pvalue for 1tailed and 2tailed tests.
Study Ch. 9.3, #4753 (4551), 5561, 6367 (5559)
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
Class Notes Homework
Oct 43:50 PM
9.2 & 9.3 Critical Value vs Pvalue Approach
Hypothesis Testing: attempt to determine if sample data is different from a previously known or expected value.
H0: = 0 Start with an assumption that sample data equals the known or expected values.
What do we use to decide?
distribution of x
x x
How do we decide? 2 different approaches
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
Class Notes Homework
Oct 43:49 PM
? G. Battaly 2019
1
PValue Approach to Hypothesis Testing
9.2 & 9.3 Critical Value vs Pvalue Approach
G. Battaly
April 01, 2019
Approach 1.
Critical Value
(table based, can use calculator)
PValue
(calculator based, can use table)
State the Null and Alternative Hypotheses: H0,Ha
2.
Decide the significance level, , and sketch
Ha: < 0
Ha: 0
Ha: > 0
/2
/2
3.
Compute the test statistic: z, t, etc.
4.
Find the critical values
Find the Pvalue
compares test statistic to critical value
z, z/2, t , t/2
compares area beyond test statistic to
5.
Decision: Rej. H0 if test
Decision: Rej. H0 if
statistic lies beyond critical
P
value in rejection region
6.
Interpret results
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
Class Notes Homework
Oct 43:49 PM
8.2 Confidence Interval: one , known
Find a CI for
Assumptions: 1. Simple Random Sample 2. nd or large n
3. known
Procedure
1. For CL of 1 find z/2 from Table II
2. Find CI:
or calculator
3. Intepret: a) If n.d., CI precise b) If not n.d., n large, CI approximate
Find a CI of 95%
CL = = 1
=
invNorm(0.025,0,1) = -1.95996 = -1.96
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
Class Notes Homework
Oct 207:28 PM
? G. Battaly 2019
2
PValue Approach to Hypothesis Testing G. Battaly
9.2 & 9.3 Critical Value vs Pvalue Approach
Pvalue Approach (digital calculator): Determine the area (p) in the tail beyond the test statistic and compare to , the area in the tail associated with the given significance level.
April 01, 2019
Shown here for righttailed test.
P
P
zt
reject H0
zt
Do NOT reject H0
p is found by:
1. calculator function or
2. normalcdf(test statistic, 9,0,1) to get area in right tail.
normalcdf(9,test statistic,0,1) to get area in left tail.
If test is 2tailed, double the result
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
Class Notes Homework
Oct 43:49 PM
9.2 & 9.3 Critical Value vs Pvalue Approach
z zt reject H0
ztzDo NOT
reject H0
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
Class Notes Homework
Oct 43:49 PM
? G. Battaly 2019
3
PValue Approach to Hypothesis Testing G. Battaly
9.2 & 9.3 Critical Value vs Pvalue Approach
PValue: observed significance 1. area in the tail beyond the test statistic 2. smallest significance level for rejecting H0
G: lefttailed test, z = 1.84
F: P
at 5% signif level, can reject H0?
P
zt
z = 1.84 P = normalcdf (_____,_____,0,1) = 0.0329 P = _______ ? 0.05 Therefore, ___________
April 01, 2019
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
Class Notes Homework
Oct 43:49 PM
9.2 & 9.3 Critical Value vs Pvalue Approach
PValue: observed significance 1. area in the tail beyond the test statistic 2. smallest significance level for rejecting H0
G: lefttailed test, z = 1.84
F: P
at 5% signif level, can reject H0?
P
zzt= 1.84
P = normalcdf (9,1.84,0,1) = 0.0329 P = 0.0329 < 0.05 Therefore, reject H0.
Further into the tail than is required by , so we have better data than is required to reject ! Our data represents a lower significance and a higher confidence: 96.7% confidence > 95% confidence
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
Class Notes Homework
Oct 43:49 PM
? G. Battaly 2019
4
PValue Approach to Hypothesis Testing G. Battaly
9.2 & 9.3 Critical Value vs Pvalue Approach
G: 2tailed test, z = 3.08
F: P
at 5% signif level, can reject H0?
zt=3.08
normalcdf (______,_____,0,1) = ______ P = 2 (________) = ______
P = _____ __ 0.05 Therefore, ___________ H0.
< >
April 01, 2019
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
Class Notes
Oct 43:49 PM
9.2 & 9.3 Critical Value vs Pvalue Approach
G: 2tailed test, z = 3.08
F: P
at 5% signif level, can reject H0?
Area in right tail Area in both tails
Note that have multiplied by 2, because it is a 2tailed test. > If you find p using normalcdf, you need to multiply by 2
for every 2tailed test. > If you use STATS/TEST, the calculator does the
multiplication.
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Statistics Home Page
Class Notes
Oct 43:49 PM
? G. Battaly 2019
5
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