Unit 4 – Inference from Data: Principles

Slides:



Advertisements
Similar presentations
Topics
Advertisements

Unit 4 – Inference from Data: Principles
HYPOTHESIS TESTING Four Steps Statistical Significance Outcomes Sampling Distributions.
Hypothesis Testing Steps of a Statistical Significance Test. 1. Assumptions Type of data, form of population, method of sampling, sample size.
Chapter 9 Hypothesis Testing.
Hypothesis testing is used to make decisions concerning the value of a parameter.
Section 9.1 Introduction to Statistical Tests 9.1 / 1 Hypothesis testing is used to make decisions concerning the value of a parameter.
Inference for Proportions(C18-C22 BVD) C19-22: Inference for Proportions.
1/2555 สมศักดิ์ ศิวดำรงพงศ์
+ Chapter 9 Summary. + Section 9.1 Significance Tests: The Basics After this section, you should be able to… STATE correct hypotheses for a significance.
CHAPTER 16: Inference in Practice. Chapter 16 Concepts 2  Conditions for Inference in Practice  Cautions About Confidence Intervals  Cautions About.
Confidence intervals are one of the two most common types of statistical inference. Use a confidence interval when your goal is to estimate a population.
CHAPTER 17: Tests of Significance: The Basics
1 Chapter 10: Introduction to Inference. 2 Inference Inference is the statistical process by which we use information collected from a sample to infer.
CHAPTER 9 Testing a Claim
Introduction to Inferece BPS chapter 14 © 2010 W.H. Freeman and Company.
Statistics 101 Chapter 10 Section 2. How to run a significance test Step 1: Identify the population of interest and the parameter you want to draw conclusions.
Ch 10 – Intro To Inference 10.1: Estimating with Confidence 10.2 Tests of Significance 10.3 Making Sense of Statistical Significance 10.4 Inference as.
Lecture PowerPoint Slides Basic Practice of Statistics 7 th Edition.
Copyright © 2011 Pearson Education, Inc. Putting Statistics to Work.
Ex St 801 Statistical Methods Inference about a Single Population Mean.
Inen 460 Lecture 2. Estimation (ch. 6,7) and Hypothesis Testing (ch.8) Two Important Aspects of Statistical Inference Point Estimation – Estimate an unknown.
Inference with Proportions Review Mr. Hardin AP STATS 2015.
AP Statistics Chapter 11 Notes. Significance Test & Hypothesis Significance test: a formal procedure for comparing observed data with a hypothesis whose.
The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers CHAPTER 9 Testing a Claim 9.2 Tests About a Population.
10.1 – Estimating with Confidence. Recall: The Law of Large Numbers says the sample mean from a large SRS will be close to the unknown population mean.
Warm Up 1. Write the four steps in writing a confidence interval and how to check conditions (step 2) for means. 2. Write the four steps involved in test.
+ Homework 9.1:1-8, 21 & 22 Reading Guide 9.2 Section 9.1 Significance Tests: The Basics.
Chapter Nine Hypothesis Testing.
Section 8.2 Day 3.
More on Inference.
Unit 5 – Chapters 10 and 12 What happens if we don’t know the values of population parameters like and ? Can we estimate their values somehow?
CHAPTER 9 Testing a Claim
Significance Test for the Difference of Two Proportions
Tests of Significance The reasoning of significance tests
Testing Hypotheses about Proportions
CHAPTER 9 Testing a Claim
STAT 312 Chapter 7 - Statistical Intervals Based on a Single Sample
CHAPTER 9 Testing a Claim
Section 8.2 Day 4.
CHAPTER 9 Testing a Claim
CHAPTER 9 Testing a Claim
Chapter 9: testing a claim
10.1: 2-Proportion Situations
More on Inference.
Unlocking the Mysteries of Hypothesis Testing
CHAPTER 9 Testing a Claim
Inference on Proportions
Chapter Nine Part 1 (Sections 9.1 & 9.2) Hypothesis Testing
Statistical Inference
YOU HAVE REACHED THE FINAL OBJECTIVE OF THE COURSE
CHAPTER 9 Testing a Claim
Confidence Intervals: The Basics
Statistical Inference for Managers
CHAPTER 9 Testing a Claim
CHAPTER 9 Testing a Claim
CHAPTER 9 Testing a Claim
Chapter 9: Testing a Claim
CHAPTER 9 Testing a Claim
CHAPTER 9 Testing a Claim
CHAPTER 16: Inference in Practice
Comparing Two Proportions
Chapter 9: Significance Testing
CHAPTER 9 Testing a Claim
CHAPTER 9 Testing a Claim
Comparing Two Proportions
CHAPTER 9 Testing a Claim
Section 11.1: Significance Tests: Basics
Statistical Test A test of significance is a formal procedure for comparing observed data with a claim (also called a hypothesis) whose truth we want to.
CHAPTER 9 Testing a Claim
Presentation transcript:

Unit 4 – Inference from Data: Principles Topics 16 - 18 Unit 4 – Inference from Data: Principles

Topic 16 Confidence Intervals: Proportion

Topic 16 - Confidence Interval: Proportion The purpose of confidence intervals is to use the sample statistic to construct an interval of values that you can be reasonably confident contains the actual, though unknown, parameter. The estimated standard deviation of the sample statistic pˆ is called the standard error of pˆ. Confidence Interval for a population proportion : where n . P^ >= 10 and n (1-p^)>= 10 Z * Critical value-Z is calculated based on level of confidence When running for example 95% Confidence Interval: 95% is called Confidence Level and we are allowing possible 5% for error, we call this alpha (α )= 5% where α is the significant level

Topic 16 - Confidence Interval: Proportion Click on STAT, TESTS and scroll down to 1-PropZint… To calculate Confidence Interval You need to have x, n and C-Level x and n comes from the sample Please note if you have p-hat and n calculate x = p-hat * n, round your answer

Exercise: 16-12: Credit Card Usage - Page 347 Exercise: 16-13: Responding to Katrina – Page 347

Watch Out A confidence interval is just that— an interval— so it includes all values between its endpoints. Do not mistakenly think that only the endpoints matter or that only the margin- of- error matters. The midpoint and actual values within the interval matter.

The margin- of- error is affected by several factors primarily A higher confidence level produces a greater margin- of- error ( a wider interval). A larger sample size produces a smaller margin- of- error ( a narrower interval). Common confidence levels are 90%, 95%, and 99%. Always check the technical conditions before applying this procedure. The sample is considered large enough for this procedure to be valid as long as npˆ>= 10 and n(1 –pˆ) >=10. If this condition is not met, then the normal approximation of the sampling distribution is not valid and the reported confidence level may not be accurate. Always consider how the sample was selected to determine the population to which the interval applies.

Choosing the sample size The confidence interval for the a Normal population will have a specified margin of error m when the sample size is If n is not a whole number then round up.

Example: Activity 16-8: Cursive Writing The number of essays needed for a 99% CI is 0.01 = 2.576 √[ (.15)(.85) /n]; n = (2.576 /.01)2 (.15)(.85) = 8460.614; n = 8461 Remember to round UP You could use a lower confidence level (95% or 90% confidence, for example), or you could use a wider margin-of-error, say .02. Either of these choices would allow you to select a smaller (random) sample.

Activity 16-11: Penny Activities - Page 347

Topic 17 - Tests of Significance: Proportions

Topic 17 – Test of Significant: Proportion A sample result that is very unlikely to occur by random chance alone is said to be statistically significant. We now formalize this process of determining whether or not a sample result provides statistically significant evidence against a conjecture about the population parameter. The resulting procedure is called a test of significance. A significance test is designed to assess the strength of evidence against the null hypothesis. Step 1: Identify and define the parameter. Step 2: we initiate hypothesis regarding the question – we can not run test of significant without establishing the hypothesis Step 3: Decide what test we have to run, in case of proportion, we use Z-test in proportion

Topic 17 – Test of Significant: Proportion Step 4: Run the test from calculator Step 5: From the calculator write down the p-value and Z-test Step 6: Compare your p-value with α – alpha – Significant Level If p-value is smaller than α we “reject” the null hypothesis, then it is statistically significant based on data. If p-value is greater than the α we “Fail to reject” the null hypothesis, then it is not statistically significant based on data. Last step: we write conclusion based on step 6 at significant level α p- value > 0.1: little or no evidence against H0 • 0.05 < p- value <= 0.10: some evidence against H0 • 0.01 < p- value <= 0.05: moderate evidence against H0 • 0.001 < p- value <= 0.01: strong evidence against H0 • p- value <= 0.001: very strong evidence against H0

Topic 17 – Test of Significant: Proportion Click on STAT, TESTS and scroll down to 1-PropZTest… To calculate One Sample Proportion Z-Test You need to have P0 , x, n and Alternative Hypothesis P0 is π0 from Null Hypothesis x and n comes from the sample Please note if you have p-hat and n calculate x = p-hat * n, round your answer Prop is the alternative hypothesis

Exercise 17-6: Properties of p-value – Page 371 Exercise 17-7: Properties of p-value – Page 371 Exercise 17-8: Wonderful Conclusions– Page 371 Exercise 17-12: Kissing Couples – Page 372 Exercise: 17-26: Employee Sick Days–Page 375 Exercise: 17-27: Stating Hypothesis –Page 375

Topic 18 More Inference Consideration

Watch Out Alpha = α A Type I error is sometimes referred to as a false alarm because the researcher mistakenly thinks that the parameter value differs from what was hypothesized. Beta = β a Type II error can be called a missed opportunity because the parameter really did differ from what was hypothesized, yet the researchers failed to realize it. 1 – β The power of a statistical test is the probability that the null hypothesis will be rejected when it is actually false ( and therefore should be rejected). Particularly with small sample sizes, a test may have low power, so it is important to recognize that failing to reject the null hypothesis does not mean accepting it as being true.