QMS 202 Lecture Notes - Lecture 5: Pooled Variance, Confidence Interval, Infor
21 Feb 2017
School
Department
Course
Professor
QMS 202
Week 5
Hypothesis Testing
- Compares the difference between the means of two independent populations
- Pooled variance t test and
- Separate variance t test
Comparing the Means of Two Independent Populations
- σ ad σ2 are known
- Z test for the difference between 2 means
- Samples are randomly and independently selected from populations that are normally
distibuted o the saple size is lage eough ,
- ̅ 1 is mean of sample 1, ̅2 is mean of sample 2
- µ1 is mean of pop. 1, µ2 is mean of pop 2
- σ2 is the variance of the pop
- z stat= (̅1- ̅2)- (µ1-µ2)/ √ σ+n1)+( σ+n2)
- The critical value Z stat follows a standardized normal distribution
- Write alt hypothesis first (H1)
CALC
- F3 Test, F1 Z, F2 2-S
- Direction of the test depends on the H1 and the way the sign goes
- Pooled off whe σ & σ kow
- Use z stat conversion formula
P Method
- P(Z<Zstat)
- F5, F1, F2
- Sigma =1
- µ =0
Difference Between 2 Means
- Population Means, independent samples
- σ ad σ ukow- POOLED variance t test
- σ ad σ KNOWN- SEPARATE variance t test
- Point estimate for the difference is ̅1- ̅2
- Goal is to test hypothesis or form of a confidence interval for the difference between 2
population means µ1-µ2
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Compares the difference between the means of two independent populations. Z test for the difference between 2 means. Samples are randomly and independently selected from populations that are normally dist(cid:396)ibuted o(cid:396) the sa(cid:373)ple size is la(cid:396)ge e(cid:374)ough (cid:894)(cid:374)(cid:1005)(cid:1096)(cid:1007)(cid:1004), (cid:374)(cid:1006)(cid:1096)(cid:1007)(cid:1004)(cid:895) (cid:454) 1 is mean of sample 1, (cid:454) 2 is mean of sample 2. 2 is the variance of the pop z stat= ((cid:454) 1- (cid:454) 2)- ( 1- 2)/ (cid:894) (cid:1005)+n1)+( (cid:1006)+n2) The critical value z stat follows a standardized normal distribution. Direction of the test depends on the h1 and the way the sign goes. (cid:1005) a(cid:374)d (cid:1006) u(cid:374)k(cid:374)ow(cid:374)- pooled variance t test. (cid:1005) a(cid:374)d (cid:1006) known- separate variance t test. Point estimate for the difference is (cid:454) 1- (cid:454) 2. Goal is to test hypothesis or form of a confidence interval for the difference between 2 population means 1- 2. Reject h0 if tstat is less than the lower critical value.
