Warm-up 9.2 Steps for a sample t-test. Answers to P6 and P7.

Slides:

Advertisements

Similar presentations

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.

Advertisements

Confidence Interval and Hypothesis Testing for:

Significance Testing Chapter 13 Victor Katch Kinesiology.

Testing means, part III The two-sample t-test. Sample Null hypothesis The population mean is equal to  o One-sample t-test Test statistic Null distribution.

Final Jeopardy $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 LosingConfidenceLosingConfidenceTesting.

Hypothesis : Statement about a parameter Hypothesis testing : decision making procedure about the hypothesis Null hypothesis : the main hypothesis H 0.

LARGE SAMPLE TESTS ON PROPORTIONS

BCOR 1020 Business Statistics Lecture 21 – April 8, 2008.

IENG 486 Statistical Quality & Process Control

Chapter 9 Hypothesis Testing.

BCOR 1020 Business Statistics Lecture 20 – April 3, 2008.

Statistics 270– Lecture 25. Cautions about Z-Tests Data must be a random sample Outliers can distort results Shape of the population distribution matters.

Significance Tests for Proportions Presentation 9.2.

Section 7-3 Hypothesis Testing for the Mean (Small Samples) Objective: SWBAT How to find critical values in a t- distribution. How to use the t-test to.

Chi-square Goodness of Fit Test

Hypothesis Testing and T-Tests. Hypothesis Tests Related to Differences Copyright © 2009 Pearson Education, Inc. Chapter Tests of Differences One.

Warm-up Day of Ch. 7 Review Free Response A h.s. math teacher believes the greater number of hours of sleep before taking an AP exam, the better the score.

Warm-up Day of 8.1 and 8.2 Quiz and Types of Errors Notes.

Claims about a Population Mean when σ is Known Objective: test a claim.

Means Tests Hypothesis Testing Assumptions Testing (Normality)

The table shows a random sample of 100 hikers and the area of hiking preferred. Are hiking area preference and gender independent? Hiking Preference Area.

Statistics Pooled Examples.

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.

More About Significance Tests

Warm-up 9.1 Confidence Interval of the Mean. Answers to H.W. 8.2 E#26 – 32 and E#34 H A : The proportion of students wearing backpacks is not 60%.

+ Chapter 9 Summary. + Section 9.1 Significance Tests: The Basics After this section, you should be able to… STATE correct hypotheses for a significance.

1 Power and Sample Size in Testing One Mean. 2 Type I & Type II Error Type I Error: reject the null hypothesis when it is true. The probability of a Type.

Chapter 9 Hypothesis Testing and Estimation for Two Population Parameters.

Student’s t-distributions. Student’s t-Model: Family of distributions similar to the Normal model but changes based on degrees-of- freedom. Degrees-of-freedom.

Section Inference for Experiments Objectives: 1.To understand how randomization differs in surveys and experiments when comparing two populations.

Warm-up 8.2 Testing a proportion Data Analysis 9 If ten executives have salaries of $80,000, six salaries of $75,000, and three have salaries of $70,000,

Chapter 12 Tests of a Single Mean When σ is Unknown.

© 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license.

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.

Warm-up Day of 8.1, 8.2, 9.1 and 9.2 Review. Answer to H.W. Problem E#17 Step 1: The amount of water in the bottles is normally distributed. A graph of.

Chapter 23 Inference for One- Sample Means. Steps for doing a confidence interval: 1)State the parameter 2)Conditions 1) The sample should be chosen randomly.

Warm-up 9.2 Steps for a sample t-test Answers to E#2 – 5 and 10 E2. a. This is an experiment, not sample, so the condition of random Assignment.

Large sample CI for μ Small sample CI for μ Large sample CI for p

Introduction to Inferece BPS chapter 14 © 2010 W.H. Freeman and Company.

JMB Ch10 Lecture 1 9th ed. v Mar 2012 EGR 252 Spring 2012 Slide 1 Statistical Hypothesis Testing  A statistical hypothesis is an assertion concerning.

Lesson Testing Claims about a Population Proportion.

1 Objective Compare of two population variances using two samples from each population. Hypothesis Tests and Confidence Intervals of two variances use.

Tests of Significance: The Basics BPS chapter 15 © 2006 W.H. Freeman and Company.

Unit 8 Section 8-3 – Day : P-Value Method for Hypothesis Testing  Instead of giving an α value, some statistical situations might alternatively.

Warm-up 9.1 Confidence Interval of the Mean. Answers to H.W. Discussion Questions.

Ex St 801 Statistical Methods Inference about a Single Population Mean.

Aim: How do we use a t-test?

Logic and Vocabulary of Hypothesis Tests Chapter 13.

Testing Hypotheses about a Population Proportion Lecture 29 Sections 9.1 – 9.3 Fri, Nov 12, 2004.

Hypothesis Testing Errors. Hypothesis Testing Suppose we believe the average systolic blood pressure of healthy adults is normally distributed with mean.

Ch8.2 Ch8.2 Population Mean Test Case I: A Normal Population With Known Null hypothesis: Test statistic value: Alternative Hypothesis Rejection Region.

Testing Hypotheses about a Population Proportion Lecture 31 Sections 9.1 – 9.3 Wed, Mar 22, 2006.

AP Process Test of Significance for 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 1 Slide © 2008 Thomson South-Western. All Rights Reserved Chapter 12 Tests of Goodness of Fit and Independence n Goodness of Fit Test: A Multinomial.

T tests comparing two means t tests comparing two means.

If we fail to reject the null when the null is false what type of error was made? Type II.

Lec. 19 – Hypothesis Testing: The Null and Types of Error.

1 Where we are going : a graphic: Hypothesis Testing. 1 2 Paired 2 or more Means Variances Proportions Categories Slopes Ho: / CI Samples Ho: / CI / CI.

SWBAT: -Determine whether to use a one or two tailed test and calculate the necessary p-value -Make and interpret a decision based on the results of a.

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

Ex St 801 Statistical Methods Part 2 Inference about a Single Population Mean (HYP)

9-2 Testing μ.

Review of Power of a Test

Significance Test for the Difference of Two Proportions

STAT 312 Chapter 7 - Statistical Intervals Based on a Single Sample

Hypothesis Testing for Proportions

Presentation transcript:

Warm-up 9.2 Steps for a sample t-test

Answers to P6 and P7

Answers to h.w. continued…

Triphammer Road Continued… Residents along Triphammer Road are displeased. The mean mph is greater than the speed limit (30 mph). To get the police involved, they’ll need to show the true mean of the speed is in fact greater than the posted mph. First, let’s calculate the test statistics. Test statistic for a proportion Test statistic for the mean

Calculating the P-value from the test statistic H o : μ = 30 mph H A : μ > 30 mph H o : μ = 30 mph H A : μ ≠ 30 mph P-value for the mean: is the probability of getting a random sample From a distribution with the mean given the null hypothesis. Based on the p-value we will reject or fail to reject the null hypothesis.

T-Test on the Calculator Fixed Level Testing is where the α is given. You reject the null Hypothesis in favor of the alternate hypothesis if your P-value is less than the level of significance.

Components of a Significance Test for a Mean pg 589 Problem: The thermostat in your classroom is set to 72 o F, but you think the thermostat isn’t working well. On seven randomly selected days you measure the temperature at your seat. Your measurements are 71, 73, 69, 68, 69, 70 and 71. Complete a significance test to determine if the temperature is different from the 72 o F set on the thermostat. Step 1: Name the test and check the conditions. Step 2: State the hypotheses. (with symbols and words)

Last Steps Step 3: Compute the statistics, P-value, and draw a sketch. Since the data is given enter the 7 temperatures under L1. Then STAT -> -> TEST, Choose T-Test with Input as Data. Step 4: Write your conclusion, summarize your findings in step 3 to support your conclusion. Use the level of significance if given to reject or fail to reject the null hypothesis. H.W. Read 9.2 Copy formulas, and terms. Complete E #17 When checking the conditions draw a graph to demonstrate the sample is approximately normal. *Bring your textbook as well. (This is part of the h.w. grade)

8.1, 8.2, 9.1 and 9.2 Notebook Check Ch.8 level of confidence(capture rate), margin of error significance test for a proportion, statistical significance, null hypothesis, alternate hypothesis, test statistic, p-value, critical values, level of significance, type 1 error, type 2 error, power of a test, one-sided, two-sided test Ch.9 Degrees of freedom, Sampling distribution for s, t-table, t-test, t-distribution, significance test for the mean. (17 terms –Ch. 8, 6 terms –Ch 9 = 23 terms at 1pt each = 23pts) Notes: 8.1, 8.1 (Day 2), 8.2, 8.2 (Day 2), 8.2 (Errors), 9.1, 9.2 ( 7 notes w/ Warm-ups 11 pts each = 77 pts) (3 pt warm-up 8 pts notes = 11 pts) 77 pts + 23 pts = 100 for Ntbk