egr 252 s09 ch.10 part 3 slide 1 statistical hypothesis testing - part 3 a statistical hypothesis...
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EGR 252 S09 Ch.10 Part 3 Slide 1
Statistical Hypothesis Testing - Part 3
A statistical hypothesis is an assertion concerning one or more populations.
In statistics, a hypothesis test is conducted on a set of two mutually exclusive statements:
H0 : null hypothesis
H1 : alternate hypothesis New test statistic of interest:
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EGR 252 S09 Ch.10 Part 3 Slide 2
Goodness-of-Fit Tests
Procedures for confirming or refuting hypotheses about the distributions of random variables.
Hypotheses:
H0: The population follows a particular distribution.
H1: The population does not follow the distribution.
Example:
H0: The data come from a normal distribution.
H1: The data do not come from a normal distribution.
EGR 252 S09 Ch.10 Part 3 Slide 3
Goodness of Fit Tests (cont.)Test statistic is χ2
Draw the picture Determine the critical value for goodness of fit test
χ2 with parameters α, ν = k – 1
Calculate χ2 from the sample
Compare χ2calc to χ2
crit
Make a decision about H0
State your conclusion.Discussion: Look at Table 10.4 in text.
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EGR 252 S09 Ch.10 Part 3 Slide 4
Tests of Independence Example: Choice of pension plan. Hypotheses
H0: Pension Plan Choice and Worker Type are independent
H1: Pension Plan Choice and Worker Type are not independent
1. Develop a Contingency Table
Worker Type
Pension Plan
Total#1 #2 #3
Salaried 160 140 40 340
Hourly 40 60 60 160
Total 200 200 100 500
EGR 252 S09 Ch.10 Part 3 Slide 5
Worker vs. Pension Plan Example
2. Calculate expected probabilities
P(#1 ∩ S) = ____________ E(#1 ∩ S) = __________
P(#1 ∩ H) = ____________ E(#1 ∩ H) = __________ (etc.)
Worker Type
Pension Plan
Total#1 #2 #3
Salaried 160 140 40 340
Hourly 40 60 60 160
Total 200 200 100 500
#1 #2 #3
S (exp.)
H (exp.)
EGR 252 S09 Ch.10 Part 3 Slide 6
Hypotheses
3. Define Hypotheses
H0: the categories (worker & plan) are independent
H1: the categories are not independent
4. Calculate the sample-based statistic
(160-136)^2/136 + (140-136)^2/136 + (40-68)^2/68 + (40-64)^2/64 + (60-64)^2/64 + (60-32)^2/32
= 49.63
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EGR 252 S09 Ch.10 Part 3 Slide 7
The Chi-Squared Test of Independence
5. Compare to the critical statistic for a test of independence, χ2α, r
where r = (a – 1)(b – 1) a = # of columnsb = # of rows
For our example, let’s use α = 0.01 _
χ20.01,2_ = 9.210 (from Table A.5, pp 756)
Comparison: χ2 calc> χ2 crit
Decision: Reject the null hypothesis
Conclusion: Worker and plan are not independent.
EGR 252 S09 Ch.10 Part 3 Slide 8