Significance Test for the Difference of Two Proportions

Slides:

Advertisements

Similar presentations

Stat 217 – Day 17 Topic 14: Sampling Distributions with quantitative data.

Advertisements

CHAPTER 7 Sampling Distributions

Quiz 6 Confidence intervals z Distribution t Distribution.

Distributions of Sample Means and Sample Proportions BUSA 2100, Sections 7.0, 7.1, 7.4, 7.5, 7.6.

UNIT FOUR/CHAPTER NINE “SAMPLING DISTRIBUTIONS”. (1) “Sampling Distribution of Sample Means” > When we take repeated samples and calculate from each one,

Sampling Distributions

The Distribution of Sample Proportions Section

AP Statistics Section 9.3A Sample Means. In section 9.2, we found that the sampling distribution of is approximately Normal with _____ and ___________.

+ The Practice of Statistics, 4 th edition – For AP* STARNES, YATES, MOORE Chapter 9: Sampling Distributions Section 9.2 Sample Proportions.

Chapter 10 – Sampling Distributions Math 22 Introductory Statistics.

Sample Variability Consider the small population of integers {0, 2, 4, 6, 8} It is clear that the mean, μ = 4. Suppose we did not know the population mean.

Sample Proportions Target Goal: I can FIND the mean and standard deviation of the sampling distribution of a sample proportion. DETERMINE whether or not.

The Sampling Distribution of

7.2: Sample Proportions.

Parameter or statistic? The mean income of the sample of households contacted by the Current Population Survey was $60,528.

© 2010 Pearson Prentice Hall. All rights reserved Chapter Sampling Distributions 8.

Chapter 7: Sampling Distributions Section 7.2 Sample Proportions.

Review Confidence Intervals Sample Size. Estimator and Point Estimate An estimator is a “sample statistic” (such as the sample mean, or sample standard.

MATH Section 4.4.

7.2 Sample Proportions Objectives SWBAT: FIND the mean and standard deviation of the sampling distribution of a sample proportion. CHECK the 10% condition.

Chapter 9 Sampling Distributions 9.1 Sampling Distributions.

Sampling Distribution of the Sample Mean

Section 6.2 Binomial Distribution

Sampling Distributions

Chapter 7: Sampling Distributions

Section 7.3 Day 2.

Comparing Two Proportions

Chapter 7 Review.

Quiz 6.1 – 6.2 tomorrow Test 6.1 – 6.2 on Monday

STANDARD ERROR OF SAMPLE

Central Limit Theorem Sample Proportions.

Warm Up Read p. 609 – Chapter 10 Intro.

CHAPTER 9 Sampling Distributions

CHAPTER 6 Random Variables

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

Section 8.2 Day 4.

Chapter 7: Sampling Distributions

Sampling Distribution of a Sample Proportion

CHAPTER 7 Sampling Distributions

Year-3 The standard deviation plus or minus 3 for 99.2% for year three will cover a standard deviation from to To calculate the normal.

CHAPTER 7 Sampling Distributions

Chapter 7: Sampling Distributions

Sampling Distribution of the Mean

Chapter 7: Sampling Distributions

Chapter 7: Sampling Distributions

CHAPTER 7 Sampling Distributions

Chapter 9: Sampling Distributions

CHAPTER 7 Sampling Distributions

Section 12.2 Comparing Two Proportions

CHAPTER 7 Sampling Distributions

Chapter 7: Sampling Distributions

Chapter 7: Sampling Distributions

Chapter 7: Sampling Distributions

CHAPTER 7 Sampling Distributions

Chapter 7: Sampling Distributions

Continuous Random Variables 2

Chapter 7: Sampling Distributions

Chapter 7: Sampling Distributions

Section 7.1 Day 3.

CHAPTER 7 Sampling Distributions

CHAPTER 7 Sampling Distributions

Chapter 7: Sampling Distributions

1/10/ Sample Proportions.

COMPARING TWO PROPORTIONS

Sampling Distributions

Warmup Which of the distributions is an unbiased estimator?

Confidence Intervals for Proportions

Section 9.2: Sample Proportions

Sample Proportions Section 9.2

Presentation transcript:

Significance Test for the Difference of Two Proportions Section 8.4 Significance Test for the Difference of Two Proportions

Quiz 8.3 – 8.4 tomorrow 1 side of a note card

Suppose: We have two populations.

Suppose: We have two populations. The proportion of successes for each population is 0.2 so …

Suppose: We have two populations The proportion of successes for each population is 0.2 so p1 = p2

Suppose: We take a pair of samples of size 30 from each population and calculate the difference in their proportions,

Suppose: We take a pair of samples of size 30 from each population and calculate the difference in their proportions, We repeat this process 5000 times

Next, we do this same process for samples of size 50 and 100 Suppose: We take a pair of samples of size 30 from each population and calculate the difference in their proportions, We repeat this process 5000 times Next, we do this same process for samples of size 50 and 100

Next, we do this same process for samples of size 50 and 100 Suppose: We take a pair of samples of size 30 from each population and calculate the difference in their proportions, We repeat this process 5000 times Next, we do this same process for samples of size 50 and 100 Where do we expect the center of the distribution to be?

Where do we expect the center of the distribution to be? 0 because p1 = p2 Recall, the mean of the differences is equal to the difference of the means.

As n1 and n2 increase? Shape: Center: Spread:

As n1 and n2 increase? Shape: more normal Center: Spread:

As n1 and n2 increase? Shape: more normal Center: stays at 0 Spread:

As n1 and n2 increase? Shape: more normal Center: stays at 0 Spread: decreases

Standard Error As n1 and n2 increase, the standard error decreases. To find standard error, use formula: SE =

Standard Error

Page 536, P48

Page 536, P48 (a) After millions of repetitions, we would expect and to both equal 0.12. Thus, the expected value of the difference of would be 0.12 - 0.12 = 0.

Page 536, P48

Page 536, P48

Page 536, P48 d. Using the calculator, normalcdf(.05,1E99, 0, .0154) gives approximately 0.00058. Note: This is not a standard normal distribution so must also use mean and standard error.

Time to go to work on Fathom Lab 8.4a! Due: Wednesday

Questions?