Testing Claims about a Population Mean Objective: test a claim.

Slides:



Advertisements
Similar presentations
Introduction to Hypothesis Testing
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.
8.3 T- TEST FOR A MEAN. T- TEST The t test is a statistical test for the mean of a population and is used when the population is normally or approximately.
Hypothesis Testing Using a Single Sample
© 2010 Pearson Prentice Hall. All rights reserved Two Sample Hypothesis Testing for Means from Independent Groups.
Business Statistics - QBM117
Hypothesis Testing Steps of a Statistical Significance Test. 1. Assumptions Type of data, form of population, method of sampling, sample size.
Chapter 11 Chi-Square Procedures 11.1 Chi-Square Goodness of Fit.
Today Today: Chapter 10 Sections from Chapter 10: Recommended Questions: 10.1, 10.2, 10-8, 10-10, 10.17,
Chapter 9 Hypothesis Testing 9.4 Testing a Hypothesis about a Population Proportion.
8-4 Testing a Claim About a Mean
Hypothesis Testing Sample Means. Hypothesis Testing for Sample Means The goal of a hypothesis test is to make inferences regarding unknown population.
11-2 Goodness-of-Fit In this section, we consider sample data consisting of observed frequency counts arranged in a single row or column (called a one-way.
8-5 Testing a Claim About a Standard Deviation or Variance This section introduces methods for testing a claim made about a population standard deviation.
The Kruskal-Wallis Test The Kruskal-Wallis test is a nonparametric test that can be used to determine whether three or more independent samples were.
7.3 Hypothesis Testing for the Mean (Small Samples) Statistics Mrs. Spitz Spring 2009.
Hypothesis Testing and T-Tests. Hypothesis Tests Related to Differences Copyright © 2009 Pearson Education, Inc. Chapter Tests of Differences One.
Hypothesis Testing Approach 1 - Fixed probability of Type I error. 1.State the null and alternative hypotheses. 2.Choose a fixed significance level α.
Claims about a Population Mean when σ is Known Objective: test a claim.
Means Tests Hypothesis Testing Assumptions Testing (Normality)
Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1 Section 7.3 Hypothesis Testing for the Mean (  Unknown).
Chapter Eleven McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Two-Sample Tests of Hypothesis Pages &
Hypothesis Testing for the Mean (Small Samples)
Section Copyright © 2014, 2012, 2010 Pearson Education, Inc. Lecture Slides Elementary Statistics Twelfth Edition and the Triola Statistics Series.
Inference about Two Population Standard Deviations.
Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 11 Section 2 – Slide 1 of 25 Chapter 11 Section 2 Inference about Two Means: Independent.
T-distribution & comparison of means Z as test statistic Use a Z-statistic only if you know the population standard deviation (σ). Z-statistic converts.
Section 9-4 Hypothesis Testing Means. This formula is used when the population standard deviation is known. Once you have the test statistic, the process.
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 10.3.
Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved Section 8-5 Testing a Claim About a Mean:  Not Known.
Chapter 9 Hypothesis Testing and Estimation for Two Population Parameters.
Hypothesis Testing with One Sample Chapter 7. § 7.3 Hypothesis Testing for the Mean (Small Samples)
1 Section 9-4 Two Means: Matched Pairs In this section we deal with dependent samples. In other words, there is some relationship between the two samples.
Slide Slide 1 Section 8-6 Testing a Claim About a Standard Deviation or Variance.
Section 10.2 Hypothesis Testing for Means (Small Samples) HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant.
Section 9.2 Hypothesis Testing Proportions P-Value.
Section 8.3 Testing the Difference Between Means (Dependent Samples)
Hypothesis Testing for the Mean (Small Samples)
1 Objective Compare of two population variances using two samples from each population. Hypothesis Tests and Confidence Intervals of two variances use.
Slide Slide 1 Section 8-4 Testing a Claim About a Mean:  Known.
STEP BY STEP Critical Value Approach to Hypothesis Testing 1- State H o and H 1 2- Choose level of significance, α Choose the sample size, n 3- Determine.
- We have samples for each of two conditions. We provide an answer for “Are the two sample means significantly different from each other, or could both.
Applied Quantitative Analysis and Practices LECTURE#14 By Dr. Osman Sadiq Paracha.
Section Copyright © 2014, 2012, 2010 Pearson Education, Inc. Lecture Slides Elementary Statistics Twelfth Edition and the Triola Statistics Series.
Testing Claims about a Population Proportion Objective: Test a claim about a population proportion.
© 2010 Pearson Prentice Hall. All rights reserved Chapter Hypothesis Tests Regarding a Parameter 10.
Tests of Significance: The Basics ESS chapter 15 © 2013 W.H. Freeman and Company.
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.
1 Section 8.5 Testing a claim about a mean (σ unknown) Objective For a population with mean µ (with σ unknown), use a sample to test a claim about the.
Created by Erin Hodgess, Houston, Texas Section 7-1 & 7-2 Overview and Basics of Hypothesis Testing.
If we fail to reject the null when the null is false what type of error was made? Type II.
Chapter 9: Hypothesis Tests for One Population Mean 9.2 Terms, Errors, and Hypotheses.
Lec. 19 – Hypothesis Testing: The Null and Types of Error.
Analysis of Variance ANOVA - method used to test the equality of three or more population means Null Hypothesis - H 0 : μ 1 = μ 2 = μ 3 = μ k Alternative.
1 Section 8.4 Testing a claim about a mean (σ known) Objective For a population with mean µ (with σ known), use a sample (with a sample mean) to test a.
Hypothesis Testing Involving One Population Chapter 11.4, 11.5, 11.2.
Chapter 7 Statistics Power Point Review Hypothesis Testing.
Section 7.3 Hypothesis Testing for the Mean (Small Samples) © 2012 Pearson Education, Inc. All rights reserved. 1 of 15.
A telephone company representative estimates that 40% of its customers have call-waiting service. To test this hypothesis, she selected a sample of 100.
Ex St 801 Statistical Methods Part 2 Inference about a Single Population Mean (HYP)
Statistics: Unlocking the Power of Data Lock 5 Section 6.6 Test for a Single Mean.
Section 8-3 Testing the Difference Between Means (Dependent Samples) We can conduct the hypothesis test on two dependent samples if ALL of the following.
Testing a Claim About a Mean:  Not Known
Chapter 9 Hypothesis Testing
Inferences on Two Samples Summary
Chapter 9 Hypothesis Testing
Hypothesis Tests for Proportions
Statistical Inference about Regression
Testing a Claim About a Standard Deviation or Variance
Inferences from Matched Pairs
Presentation transcript:

Testing Claims about a Population Mean Objective: test a claim

 Student’s t-distribution with n-1 degrees of freedom  List properties:

1. Determine the null and alternative hypotheses 2. Select a level of significance 3. Compute the test statistic 4. Determine the critical value 5. Compare the critical value with the test statistic Reject the null hypothesis if the test statistic falls within the critical region!! 6. State the conclusion

Test the weight of Skittles as if you were a quality-control engineer. Because shutting down the plant is very expensive, test the claim at 0.01 level of significance.

The US Golf Association requires that golf balls have a diameter that is 1.68 inches. An engineer wishes to discover whether Maxfli XS golf balls have a mean diameter different from 1.68 inches. A random sample of Maxfli XS golf balls was selected

(1) State the null and alternative hypotheses H 0 : μ=1.68H 1 : μ≠1.68 (2) Select α α=0.05 (3) Find the t-score t0=t0= (4) Find the critical value (4) Determine p-value t 0.05/2 =±2.201 p= (5) Compare t-score (5) Compare p-value to critical value to α 0.77 < 2.201,so do not reject H < , so do not reject H 0 (6) State the conclusion There is not sufficient evidence to support the claim that the diameter of the golf balls does not equal 1.68.

 If using the calculator, you can have the calculator do a t-test, which will give the p- value. You compare it to the level of significance.  Reject the null hypothesis if the p-value < α.  Assignment: page 5381 – 8, 13, 15, 23