ioe265f11-Lec20

# ioe265f11-Lec20 - Lec20 - Two Sample Hypothesis Tests...

This preview shows pages 1–6. Sign up to view the full content.

Lec20 - Two Sample Hypothesis Tests IOE 265 F11 1 1 Two-Sample Hypothesis Tests 2 Topics I. Two Sample Mean Tests II. Test of Two Proportions III. F-Test (2 Variances)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Lec20 - Two Sample Hypothesis Tests IOE 265 F11 2 3 I. Two Sample Mean Tests Case USE Test Statistic Formula I known ’s , and normal populations z o II unknown ’s , and normal populations (unequal variances) t o III t o Tests of Two Population Means n m y x z 2 2 2 1 0 n s m s y x t 2 2 2 1 0 unknown ’s , and normal populations (equal variances) n m s y x t p 1 1 2 0 IV t o Paired t-test n s d t d 0 4 Case I: Two-Sample Z Test Z Tests and Confidence Intervals for a Difference between the means of two different population distributions: 1 - 2 Assumptions: X i ’s are a random sample from a population with mean 1 and variance 1 2 Y i ’s are a random sample from a population with mean 2 and variance 2 2 The X i ’s and Y i ’s are independent from one another The variances of both populations are known
Lec20 - Two Sample Hypothesis Tests IOE 265 F11 3 5 2 Sample Z test Since both populations are normal, then X-bar and Y-bar are also normal and we can get the following standard normal variable:        n m Y X Y X Z Y X 2 2 2 1 2 1 2 2 1 samples Y of Number samples X of Number n m 6 Z test If we set the difference between the population means as: Null Hypothesis: Test statistic: Alternative Hypothesis: 2 1 0 0 2 1 0 : H n m y x z 2 2 2 1 0 2 2 0 2 1 0 2 1 0 2 1 or : : : z z z z H z z H z z H a a a

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Lec20 - Two Sample Hypothesis Tests IOE 265 F11 4 7 P-Values The P-value (or observed significance level) is the smallest level of significance (probability) at which H 0 would be rejected when a specified test procedure is used on a given data set. Basic rules: The bigger the P-value, the higher the chance of a type I error for the calculated test statistic (e.g. z 0 or t 0 ). Therefore, we should not reject H 0 The smaller the P-value, the lower the chance of a type I error. Therefore, we should reject H 0 level) (at reject 0 H value P level) (at reject not do 0 H value P 8 What is the P-value then? It is customary to call the data significant when H 0 is rejected and not significant when we fail to reject H 0 The p-value is then the tail area captured by the computed value of the test statistic (e.g. z 0 or t 0 )
Lec20 - Two Sample Hypothesis Tests IOE 265 F11 5 9 P-Value Areas (Z test) z 0 Upper-Tailed Lower-Tailed z 0 Two-Tailed -z 0 z 0   0 1 z value P   0 z value P   0 1 2 z value P 10 Z test - Example The drying times for two formulations of paint are tested: standard vs. express. It is known that the population standard deviation

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## ioe265f11-Lec20 - Lec20 - Two Sample Hypothesis Tests...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online