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

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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

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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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