Inference Concepts 1-Sample Z-Tests.

Slides:



Advertisements
Similar presentations
There are two statistical tests for mean: 1) z test – Used for large samples (n ≥ 30) 1) t test – Used for small samples (n < 30)
Advertisements

Statistical Significance What is Statistical Significance? What is Statistical Significance? How Do We Know Whether a Result is Statistically Significant?
Probability & Statistical Inference Lecture 7 MSc in Computing (Data Analytics)
HYPOTHESIS TESTING Four Steps Statistical Significance Outcomes Sampling Distributions.
Statistical Significance What is Statistical Significance? How Do We Know Whether a Result is Statistically Significant? How Do We Know Whether a Result.
Inferences About Means of Single Samples Chapter 10 Homework: 1-6.
Inferences About Means of Single Samples Chapter 10 Homework: 1-6.
Chapter 3 Hypothesis Testing. Curriculum Object Specified the problem based the form of hypothesis Student can arrange for hypothesis step Analyze a problem.
Chapter 12 Inferring from the Data. Inferring from Data Estimation and Significance testing.
Quantitative Business Methods for Decision Making Estimation and Testing of Hypotheses.
Correlation & Regression
Hypothesis Testing and T-Tests. Hypothesis Tests Related to Differences Copyright © 2009 Pearson Education, Inc. Chapter Tests of Differences One.
Hypothesis Testing with Two Samples
1 © Lecture note 3 Hypothesis Testing MAKE HYPOTHESIS ©
CHAPTER 2 Statistical Inference 2.1 Estimation  Confidence Interval Estimation for Mean and Proportion  Determining Sample Size 2.2 Hypothesis Testing:
Mid-semester feedback In-class exercise. Chapter 8 Introduction to Hypothesis Testing.
Chapter 8 Introduction to Hypothesis Testing
Claims about a Population Mean when σ is Known Objective: test a claim.
Chapter 9 Hypothesis Testing II: two samples Test of significance for sample means (large samples) The difference between “statistical significance” and.
Instructor Resource Chapter 5 Copyright © Scott B. Patten, Permission granted for classroom use with Epidemiology for Canadian Students: Principles,
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Chapter 12 Inference About A Population.
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 10.17:
Chapter 9 Introduction to the t Statistic. 9.1 Review Hypothesis Testing with z-Scores Sample mean (M) estimates (& approximates) population mean (μ)
Slide Slide 1 Section 8-4 Testing a Claim About a Mean:  Known.
MeanVariance Sample Population Size n N IME 301. b = is a random value = is probability means For example: IME 301 Also: For example means Then from standard.
: An alternative representation of level of significance. - normal distribution applies. - α level of significance (e.g. 5% in two tails) determines the.
Logic and Vocabulary of Hypothesis Tests Chapter 13.
© Copyright McGraw-Hill 2004
T-TestsSlide #1 1-sample t-test H o :  =  o (where  o = specific value) Statistic: Test Statistic: Assume: –  is UNknown – n is large (so that the.
Goodness-of-FitSlide #1 Goodness-of-Fit Test Examples – –Test whether responses are “random” (e.g., preference) –Test Mendelian genetics (e.g., 3:1 and.
- 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.
Inferences Concerning Variances
Ch8.2 Ch8.2 Population Mean Test Case I: A Normal Population With Known Null hypothesis: Test statistic value: Alternative Hypothesis Rejection Region.
Applied Quantitative Analysis and Practices LECTURE#14 By Dr. Osman Sadiq Paracha.
T-TestsSlide #1 2-Sample t-test -- Examples Do mean test scores differ between two sections of a class? Does the average number of yew per m 2 differ between.
Inference ConceptsSlide #1 1-sample Z-test H o :  =  o (where  o = specific value) Statistic: Test Statistic: Assume: –  is known – n is “large” (so.
HYPOTHESES TESTING. Concept of Hypotheses A hypotheses is a proposition which the researcher wants to verify. It may be mentioned that while a hypotheses.
Ex St 801 Statistical Methods Part 2 Inference about a Single Population Mean (HYP)
Introduction For inference on the difference between the means of two populations, we need samples from both populations. The basic assumptions.
More on Inference.
Inference for the Mean of a Population
Lecture Nine - Twelve Tests of Significance.
One-Sample Inference for Proportions
Hypothesis Testing I The One-sample Case
Hypothesis Testing.
STAT 312 Chapter 7 - Statistical Intervals Based on a Single Sample
Math 4030 – 10b Inferences Concerning Variances: Hypothesis Testing
Chapter Six Normal Curves and Sampling Probability Distributions
When we free ourselves of desire,
CONCEPTS OF HYPOTHESIS TESTING
Hypothesis Tests for a Population Mean in Practice
More on Inference.
Statistical Inference for the Mean Confidence Interval
Inferences on Two Samples Summary
9 Tests of Hypotheses for a Single Sample CHAPTER OUTLINE
Chapter 9: Hypothesis Tests Based on a Single Sample
Hypothesis Tests for Proportions
Recipe for any Hypothesis Test
Hypothesis Tests One Sample Means
Statistical Inference about Regression
Sampling Distributions
AP STATISTICS LESSON 10 – 2 (DAY 3)
Hypothesis Tests for a Standard Deviation
CHAPTER 12 Inference for Proportions
CHAPTER 12 Inference for Proportions
Chapter 24 Comparing Two Means.
Testing Hypotheses I Lesson 9.
Testing Hypotheses about a Population Proportion
Hypothesis Testing for Proportions
Presentation transcript:

Inference Concepts 1-Sample Z-Tests

Recipe for any Hypothesis Test 1) State the rejection criterion (a) 2) State the null & alternative hypotheses and define the parameter(s) 3) Determine which test to perform – Explain! 4) Collect the data (address type of study and randomization) 5) Check all necessary assumption(s) 6) Calculate the appropriate statistic(s) 7) Calculate the appropriate test statistic 8) Calculate the p-value 9) State your rejection decision 10) Summarize your findings in terms of the problem 11) If rejected H0, compute a 100(1-a)% confidence region for parameter Inference Concepts

1-sample Z-test Ho: m = mo (where mo = specific value) Statistic: Test Statistic: Assume: s is known n is “large” (so sampling distribution is Normal) When: One population, quantitative variable, s is known. Inference Concepts

Full Example The mean number of close friends for the population of people living in the U.S. is 5.7. The standard deviation in this slightly skewed population is 1.3. An investigator predicts that the mean number of close friends for introverts will be significantly different from the mean of the general population. The mean number of close friends for a random sample of 26 introverts is 6.5. Do these data support, at the 5% level, the investigator's prediction? Inference Concepts