Week 5 - 2 proportions Ch 10.3 LAST HANDOUT FOR EXAM 1.doc - Section 10.3 Inference about the Difference Between Two Population Proportions LAST HANDOUT

Week 5 - 2 proportions Ch 10.3 LAST HANDOUT FOR EXAM 1.doc...

This preview shows page 1 - 3 out of 6 pages.

Section 10.3 Inference about the Difference Between Two Population Proportions LAST HANDOUT FOR EXAM 1 Goals for CH 10.3: 1) Hypothesis test for two proportions 2) Confidence interval for two proportions Comparing two populations containing qualitative ( categorical) data When data are qualitative, we can only count the number of times each value of the variable occurs. From these counts , we compute proportions (or percentages). Parameter of interest is the difference between two population proportions: (p 1 – p 2 ) . Hypothesis Testing for the Difference Between Two Population Proportions : Test statistic : Z = n 1 = # of observations in sample 1 p 1 = pop. proportion in population 1 1 ˆ p = sample proportion in sample 1 n 2 = # of observations in sample 2 p 2 = pop. proportion in population 2 2 ˆ p = sample proportion in sample 2 Hypotheses : I. H o : ( p 1 p 2 ) = 0 vs. H A : ( p 1 p 2 ) 0 II . H o : ( p 1 p 2 ) = 0 vs. H A : ( p 1 p 2 ) > 0 which p is larger in this Ha? __P 1 ___ III . H o : ( p 1 p 2 ) = 0 vs. H A : ( p 1 p 2 ) < 0 Q: After completing your analyses, will you know the true values of p 1 and p 2 ? NO (FALSE) Q: The H o above implies that the two proportions are ______ EQUAL _______. Q: If you reject H o and go with the alternative: H A : p 1 p 2 < 0. Which proportion is larger? _P2___ Since the initial values of p 1 and p 2 are unknown we will define n 1 and n 2 as sufficiently large if n 1 1 ˆ p , n 1 (1- 1 ˆ p ) , n 2 2 ˆ p , n 2 (1- 2 ˆ p ) are all greater than or equal to 5. Conditions for inference on P (Assumptions) The data are from SRS’s from the populations of interest 1 2 2 2 1 1 1 2 1 2 1 ) ˆ 1 ( ˆ ) ˆ 1 ( ˆ ) ( ) ˆ ˆ ( n p p n p p p p p p
Image of page 1
The sample sizes n 1 and n 2 are large enough (i.e. sufficiently large)
Image of page 2
Image of page 3

You've reached the end of your free preview.

Want to read all 6 pages?

  • Spring '17
  • mr. smith

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes