Unit 7 Sampling Distributions. SizeMean (yrs)Stdev (yrs) Population12.269.61 n = 412.314.80 n = 1612.242.32 n = 4912.291.30.

Slides:

Advertisements

Similar presentations

Happiness comes not from material wealth but less desire.

Advertisements

THE CENTRAL LIMIT THEOREM

How many movies do you watch? Does the CLT apply to means?  The Central Limit Theorem states that the more samples you take, the more Normal your.

Sampling Distributions Martina Litschmannová K210.

THE CENTRAL LIMIT THEOREM The “World is Normal” Theorem.

Sampling distributions. Example Take random sample of students. Ask “how many courses did you study for this past weekend?” Calculate a statistic, say,

Distribution of Sample Means, the Central Limit Theorem If we take a new sample, the sample mean varies. Thus the sample mean has a distribution, called.

5.3 The Central Limit Theorem. Roll a die 5 times and record the value of each roll. Find the mean of the values of the 5 rolls. Repeat this 250 times.

DISTRIBUTION OF THE SAMPLE MEAN

Lesson #17 Sampling Distributions. The mean of a sampling distribution is called the expected value of the statistic. The standard deviation of a sampling.

Introduction to Probability and Statistics Chapter 7 Sampling Distributions.

6-5 The Central Limit Theorem

Chapter 11: Random Sampling and Sampling Distributions

Sample Distribution Models for Means and Proportions

Chapter 9 Day 4.

1 Ch5. Probability Densities Dr. Deshi Ye

Sampling Variability and Sampling Distributions How can a sample be used to accurately represent the characteristics of a population?

INFERENCE ABOUT MEANS Chapter 23. CLT!! If our data come from a simple random sample (SRS) and the sample size is sufficiently large, then we know the.

Sampling Distributions. Parameter A number that describes the population Symbols we will use for parameters include  - mean  – standard deviation.

The Central Limit Theorem. 1. The random variable x has a distribution (which may or may not be normal) with mean and standard deviation. 2. Simple random.

In this chapter we will consider two very specific random variables where the random event that produces them will be selecting a random sample and analyzing.

A spinner from a board game randomly indicates a real number between 0 and 50. The spinner is fair in the sense that it indicates a number in a given interval.

1 Chapter 5 Sampling Distributions. 2 The Distribution of a Sample Statistic Examples  Take random sample of students and compute average GPA in sample.

The Normal Distribution. Bell-shaped Density The normal random variable has the famous bell-shaped distribution. The most commonly used continuous distribution.

AP Statistics 9.3 Sample Means.

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

Sampling Distribution of a sample Means

Chapter 18 – Part II Sampling Distribution for the Sample Mean.

Chapter 6 Lecture 3 Sections: 6.4 – 6.5.

Sample Means: Target Goal: I can find the mean and standard deviation of the sampling distribution. 7.3a h.w: pg 441:43 – 46; pg 454: 49, 51, 53, 55.

Sampling and sampling distibutions. Sampling from a finite and an infinite population Simple random sample (finite population) – Population size N, sample.

AP STATISTICS LESSON SAMPLE MEANS. ESSENTIAL QUESTION: How are questions involving sample means solved? Objectives:  To find the mean of a sample.

Population distribution VS Sampling distribution

 A probability function is a function which assigns probabilities to the values of a random variable.  Individual probability values may be denoted by.

Section 5.2 The Sampling Distribution of the Sample Mean.

Sampling Distribution of a Sample Mean Lecture 30 Section 8.4 Mon, Mar 19, 2007.

Central Limit Theorem-CLT MM4D1. Using simulation, students will develop the idea of the central limit theorem.

Statistics 300: Elementary Statistics Section 6-5.

Chapter 7: Introduction to Sampling Distributions Section 2: The Central Limit Theorem.

The Central Limit Theorem 1. The random variable x has a distribution (which may or may not be normal) with mean and standard deviation. 2. Simple random.

1 BA 275 Quantitative Business Methods Quiz #2 Sampling Distribution of a Statistic Statistical Inference: Confidence Interval Estimation Introduction.

Confidence intervals. Want to estimate parameters such as  (population mean) or p (population proportion) Obtain a SRS and use our estimators, and Even.

Topic 5 - Joint distributions and the CLT

1 Sampling distributions The probability distribution of a statistic is called a sampling distribution. : the sampling distribution of the mean.

Chapter 18: The Central Limit Theorem Objective: To apply the Central Limit Theorem to the Normal Model CHS Statistics.

1 Probability and Statistics Confidence Intervals.

Central Limit Theorem Let X 1, X 2, …, X n be n independent, identically distributed random variables with mean  and standard deviation . For large n:

Sampling Distributions

Example A population has a mean of 200 and a standard deviation of 50. A random sample of size 100 will be taken and the sample mean x̄ will be used to.

Chapter 7 Review.

Chapter 8 Sampling Distributions. Parameter A number that describes the population Symbols we will use for parameters include  - mean  – standard.

Chapter 8 Lesson 8.2 Sampling Variability and Sampling Distributions 8.2: The Sampling Distribution of a Sample Mean.

Chapter 8 Lesson : The Sampling Distribution of a Sample Mean

Central Limit Theorem-CLT

THE CENTRAL LIMIT THEOREM

Sampling Distribution of a sample Means

Applications…….

Chapter 8 Sampling Variability and Sampling Distributions

Chapter 7 ENGR 201: Statistics for Engineers

THE CENTRAL LIMIT THEOREM

Distribution of the Sample Proportion

Lecture Slides Elementary Statistics Twelfth Edition

Chapter 3: Averages and Variation

9.3 Sample Means.

Section 9.3 Distribution of Sample Means

Suppose that the random variable X has a distribution with a density curve that looks like the following: The sampling distribution of the mean of.

7.3 Sample Means HW: p. 454 (49-63 odd, 65-68).

Notes: Sample Means

Introduction to Sampling Distributions

The Normal Distribution

Presentation transcript:

Unit 7 Sampling Distributions

SizeMean (yrs)Stdev (yrs) Population n = n = n =

#Mathematics_as_science

 But most population distributions are not approximately normal.

Example 1: Soda cans are filled such that the volume is approx. normally dist. with a mean of 12 oz and a stdev of 0.15 oz. Suppose we select 16 cans and find an average volume of oz. Is this unusual?

Example 2: Acme Fasteners Co. produces bolts which are supposed to have a mean diameter of 0.5 inches and a standard deviation of 0.02 inches.

Example 2, con’t: The machine will be shut down and recalibrated if the mean diameter of the bolts is less than 0.49 or greater than 0.51 inches.

Example 2, con’t: Suppose you take a sample of 37 bolts. What is the approx. probability that the machine will be shut down unnecessarily?

Example 3: Suppose that the weights of people are approx. normally distr. with mean 164 lbs and stdev 23 lbs. 16 people get on an elevator which states the following:

Example 3, con’t: “No more than 16 persons. Weight limit 2500 lbs.” What is the approx. prob. that the elevator will be over the limit?

Example 4: Mini-Mart receipts show that customer purchases have a skewed dist. with mean $32 and stdev $20.

Example 4, con’t: What is the prob. that one customer will make a purchase greater than $40?

Example 4, con’t: Is it likely that the next 50 customers will spend an average of at least $40?

Example 5: Pollution (CO emissions) for a specific make and model of a car vary with a mean of 2.9 g/mile and a stdev of 0.4 g/mile. Your company owns 8 of these cars. BVD p. 430

Example 5, con’t: Say your 8 cars get an average of 2.75 g/mile of CO emissions. Is this unusual? BVD p. 430