### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Leson STP 231

ASU

### View Full Document

## 53

## 1

1 review

## Popular in Statistics for Biosciences

## Popular in Statistics

This 5 page Class Notes was uploaded by Mile on Monday October 26, 2015. The Class Notes belongs to STP 231 at Arizona State University taught by in Fall 2015. Since its upload, it has received 53 views. For similar materials see Statistics for Biosciences in Statistics at Arizona State University.

## Reviews for Leson

I'm a really bad notetaker and the opportunity to connect with a student who can provide this help is amazing. Thank you so much StudySoup, I will be back!!!

-*Darrion Kulas*

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/26/15

Sampling Error 0 Sampling error An error that occurs when we use samples to estimate a population characteristic Defining Sampling Distribution 0 Sampling distribution of a statistic Probability distribution that specifies probabilities for all possible values the statistic can take 0 Capital X is now a statistic or sampling distribution of sample mean Simple Illustrative Example 0 The random variable of the population is the number of meals per day A population consists of 4 people Number of meals per day 1 3 5 and 7 The population mean Construct the sampling distribution of the sample mean for Samples IU39ICJO a random samples of size 1 b random samples of size 2 c random samples of size 3 d random samples of size 4 e For sample of each size find the probability the sample mean will be equal to the population mean D For sample of each size find the probability the sampling error made in estimating the population mean by the sample mean will be 1 or less Using the number 1 3 5 7 I n 1 I X 2 sample mean Sampling distribution is made up of the sample mean and probability Sample mean Probability 1 14 3 14 5 14 7 14 o All possible samples when sample size is 2 n2 0 1 3 o 1 5 o 1 7 O 3 5 O 3 7 O 5 7 Samples Sample mean Probability 13 2 16 15 3 16 17 4 16 35 4 16 37 5 16 57 6 16 0 Could combine the samples 17 and 35 0 Their probability would become 26 or 13 0 Sampling distribution of sample mean X Probability 2 16 3 16 4 13 5 16 6 16 Sampling distribution of sampling mean for sample sizes of 3 n3 Samples Sample Mean Probability 135 3 14 137 113 36667 14 157 133 43333 14 357 5 14 0 Remember average or mean is addition of all values and divided by number of values 0 Allvalues1359 0 Number of Values 3 I 93 3 For sample size 4 0 There is only one possible sample 135 The sample mean is 4 0 We can obtain population standard deviation I ll 2 4 u o 2 Square root of Zxi u2 N u 2236068 39 HXbar 4 lJ I O39X bar 1290994 uxbar is the mean of the sample mean oxbar is the standard deviation of the sample mean u The quotXquot in Xbar is capitalized This is because it is treating the sample mean as a random variable Square root of NnN1 oSqrtn For this problem I Sqrt4241 2236068Sqrt2 Our Findings 0 HXbar 4 lJ o oxbar Square root of NnN1 oSqrtn 0 Where N4 n1 2 3 4 I 4 022236068 Sample size HXbar GXbar 1 4 2236068 2 4 1290994 3 4 0745356 4 4 0 Sampling Distribution of the Sample Mean 0 Suppose the population mean is u and population standard deviation is G then the sampling distribution of the sample mean has mean ux bar u and standard deviation oxbar oSqrtn 0 When population reaches sample size their values become exactly the same Example 0 Based on census information The total income in a household in Ohio has a mean of 46000 and a standard deviation of 10000 0 For samples of size 100 find the mean and standard deviation of all possible sample means Solution 0 For the sampling distribution of the sample mean the center is 46000 and the variability is 10000sqrt100 1000 Central Limit Theorem 0 For random sample of sufficiently large size the sampling distribution of the sample mean is approximately normal with mean u and standard deviation osqrtn Central Limit Theorem Conditions 0 Randomization Data values must be sampled randomly 0 Independence assumption The sampled values must be mutually independent 0 10 rule The sample is no more than 10 of the population Large enough sample 0 The sample size must be at least 30 u If we were to draw a curve to fit the information it will be a symmetric normal curve Each number represents a sample mean of one of the many samples selected I When we put all of these sample means together we make the sample normal distribution curve Follows 39 llXbar I GXbar

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.