Section 10.4 Hypothesis Testing for Population Proportions HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant.

Slides:



Advertisements
Similar presentations
Section 10.2 Hypothesis Testing for Means (Small Samples) HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant.
Advertisements

Testing a Claim about a Proportion Assumptions 1.The sample was a simple random sample 2.The conditions for a binomial distribution are satisfied 3.Both.
Independent Samples: Comparing Proportions Lecture 35 Section 11.5 Mon, Nov 20, 2006.
Two Sample Hypothesis Testing for Proportions
© 2010 Pearson Prentice Hall. All rights reserved Hypothesis Testing Using a Single Sample.
HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Chapter 12 Additional.
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 8-1 Business Statistics: A Decision-Making Approach 6 th Edition Chapter.
8-3 Testing a Claim about a Proportion
Copyright © 2014, 2013, 2010 and 2007 Pearson Education, Inc. Chapter Hypothesis Tests Regarding a Parameter 10.
Definitions In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test is a standard procedure for testing.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Statistics for Business and Economics 8 th Edition Chapter 9 Hypothesis Testing: Single.
Significance Tests for Proportions Presentation 9.2.
HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Chapter 14 Analysis.
Confidence Intervals and Hypothesis Testing - II
Testing Hypotheses about a Population Proportion Lecture 29 Sections 9.1 – 9.3 Tue, Oct 23, 2007.
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap th Lesson Introduction to Hypothesis Testing.
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 10.4.
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 10.2.
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 10.1.
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 10.7.
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 10.3.
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 10.2.
Section 10.3 Hypothesis Testing for Means (Large Samples) HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant.
Hypothesis Testing for Proportions
1 Introduction to Hypothesis Testing. 2 What is a Hypothesis? A hypothesis is a claim A hypothesis is a claim (assumption) about a population parameter:
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 10.6.
Section 12.1 Scatter Plots and Correlation HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems,
Copyright © Cengage Learning. All rights reserved. 10 Inferences Involving Two Populations.
When should you find the Confidence Interval, and when should you use a Hypothesis Test? Page 174.
Section 8.2 Estimating Population Means (Large Samples) HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant.
Section 10.1 Fundamentals of Hypothesis Testing HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems,
Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved Section 8-3 Testing a Claim About a Proportion.
Section 8.4 Estimating Population Proportions HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems,
Copyright © 2013, 2010 and 2007 Pearson Education, Inc. Section Inference about Two Means: Independent Samples 11.3.
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 10.4.
Section 10.2 Hypothesis Testing for Means (Small Samples) HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant.
Section 10.3 Hypothesis Testing for Means (Large Samples) HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant.
Section 9.2 Hypothesis Testing Proportions P-Value.
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 10.17:
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 10.3.
Section 7.2 Central Limit Theorem with Population Means HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant.
Copyright © 2011 Pearson Education, Inc. Putting Statistics to Work.
Section 8.4 Estimating Population Proportions HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems,
Testing Hypotheses about a Population Proportion Lecture 29 Sections 9.1 – 9.3 Fri, Nov 12, 2004.
Testing Hypotheses about a Population Proportion Lecture 29 Sections 9.1 – 9.3 Wed, Nov 1, 2006.
Testing Hypotheses about a Population Proportion Lecture 31 Sections 9.1 – 9.3 Wed, Mar 22, 2006.
Testing Claims about a Population Proportion Objective: Test a claim about a population proportion.
1 Definitions In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test is a standard procedure for testing.
Section 10.5 Types of Errors HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc. All rights.
Major Steps. 1.State the hypotheses.  Be sure to state both the null hypothesis and the alternative hypothesis, and identify which is the claim. H0H0.
Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 11 Section 3 – Slide 1 of 27 Chapter 11 Section 3 Inference about Two Population Proportions.
Section 8.3 Estimating Population Means (Small Samples) HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant.
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 10.5.
Hypothesis Tests Hypothesis Tests Large Sample 1- Proportion z-test.
© 2010 Pearson Prentice Hall. All rights reserved Chapter Hypothesis Tests Regarding a Parameter 10.
Hypothesis Testing – Two Means(Small, Independent Samples)
Section 8.2 Day 3.
Hypothesis Testing – Two Population Variances
Hypothesis Testing for Means (Small Samples)
Hypothesis Testing for Proportions
Multiple Regression Equations
Testing Hypotheses about a Population Proportion
Fundamentals of Hypothesis Testing
Hypothesis Testing for Population Means (s Unknown)
MATH 2311 Section 8.2.
Hypothesis tests for the difference between two proportions
Hypothesis Tests for Proportions
Hypothesis Tests for Two Population Standard Deviations
Testing Hypotheses about a Population Proportion
Testing Hypotheses about a Population Proportion
Presentation transcript:

Section 10.4 Hypothesis Testing for Population Proportions HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.

How this lesson fits in Previous lessons Hypothesis testing for a population mean, μ, at some level of significance, α Traditional method with a critical value and a test value Or p-value method with a test value and its probability: is p < α? If so, then reject H 0. This lesson Hypothesis testing for a population proportion, p, at some level of significance, α Traditional method could be used but Hawkes doesn’t do any this way Hawkes uses p-value method only, and it works the same way (added content by D.R.S.)

How this lesson fits in Previous lessons We used either the t test or the z test, depending on the sample size (if n<30 then t; if n≥30, then z) We used TI-84 TESTS T-Test and Z-Test. This lesson For proportions, we always talk in z language We never see t with proportions testing We use TI-84 TESTS 1-PropZTest. (added content by D.R.S.)

HAWKES LEARNING SYSTEMS math courseware specialists Test Statistic for Population Proportion: Hypothesis Testing 10.4 Hypothesis Testing for Population Proportions The following conditions must be met: 1. np ≥ 5 2. n(1 – p) ≥ 5 p (without the hat) Is the population proportion in the null hypothesis These fine-print conditions enforce the notion that “if the proportion is an extreme one, you need a larger Sample size.”

Proportions have an “either-or” aspect to them p is always between 0 and 1. – Numerator: how many have the characteristic – Denominator: how many in total If p is the proportion that has some characteristic, then (1 – p) is the proportion that doesn’t have that characteristic. p + (1 – p) = 1 probabilities always sum to 1 Sometimes you see it written as q: q = 1 – p (added content by D.R.S.)

Examples of proportions p = proportion that… p = proportion in favor of the candidate p = proportion of patients who were helped by the treatment p = proportion of dogs who have a certain gene in their DNA p = proportion of defective units we manufactured 1 – p = proportion that… 1 – p = proportion not in favor of the candidate 1 – p = proportion of patients who didn’t benefit from the treatment 1 – p = proportion of dogs who don’t have a certain gene in their DNA 1 – p = proportion of good units we manufactured (Added content by D.R.S.)

HAWKES LEARNING SYSTEMS math courseware specialists Conclusions for a Hypothesis Testing Using p-Values: 1.If pValue of the z test statistic ≤ , then reject the null hypothesis. 2.If pValue of the z test statistic > , then fail to reject the null hypothesis. Hypothesis Testing 10.4 Hypothesis Testing for Population Proportions CAUTION ! CAUTION !! CAUTION !!! If you see something like “p < α”, it is referring to the p Value of the computed test statistic z, which is Not The Same as the “p” proportion value.

HAWKES LEARNING SYSTEMS math courseware specialists Steps for Using p-Values in Hypothesis Testing: 1.State the null and alternative hypotheses. 2.Set up the hypothesis test by choosing the test statistic and stating the level of significance. 3.Gather data and calculate the necessary sample statistics. 4.Draw a conclusion by comparing the p-value to the level of significance. Hypothesis Testing 10.4 Hypothesis Testing for Population Proportions

HAWKES LEARNING SYSTEMS math courseware specialists Draw a conclusion: The local school board has been advertising that at least 65% of voters favor a tax increase to pay for a new school. A local politician believes that less than 65% of his constituents favor this tax increase. To test his claim, he asked 50 of his constituents whether they favor the tax increase and 27 said that they would vote in favor of the tax increase. If the politician wishes to be 95% confident in his conclusion, does this information support his claim? Solution: First state the hypotheses: H0:H0: Ha:Ha: Next, set up the hypothesis test and state the level of significance: c  0.95,   0.05 np  50(0.65)  32.5  ≥ 5, n(1 – p)  50(0.35)  17.5 ≥ 5 Reject if p (of the test statistic) < , or if p < p ≥ 0.65 p < 0.65 Hypothesis Testing 10.4 Hypothesis Testing for Population Proportions

HAWKES LEARNING SYSTEMS math courseware specialists Solution (continued): Gather the data and calculate the necessary sample statistics: n  50, p  0.65, .54, Since this is a left-tailed test, p  Finally, draw a conclusion: Since p is greater than , we will fail to reject the null hypothesis. The evidence does not sufficiently support the politician’s claim that less than 65% of the constituents favor a tax increase to pay for a new school. –1.63 Hypothesis Testing 10.4 Hypothesis Testing for Population Proportions

TI-84 1-PropZTest Inputs p 0 is the proportion in the null hypothesis x = how many in the sample had the characteristic n = sample size overall ≠ or p 0 is the alternative hypothesis Highlight Calculate and press ENTER (added content by D.R.S.)

TI-84 1-PropZTest Outputs prop <.65 is the H a z = the Test Statistic (from the big formula) p = the p-value of that z – Compare that to the α – Is it <α ? Then reject H 0. p_hat is the sample proportion, = x / n n = sample size n (added content by D.R.S.)