### Create a StudySoup account

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

Already have a StudySoup account? Login here

# Class Note for ECON 2370 at UH

### View Full Document

## 15

## 0

## Popular in Course

## Popular in Department

This 6 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 15 views.

## Reviews for Class Note for ECON 2370 at UH

### 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: 02/06/15

Econ 2370 Spring 2000 O Donnell d lentral Limit Theorem if the sample size is large eg if n is large the sampling distribution will be approximately normal If the sample is normal we have a large set of statistical tools to our disposal 3 Types of estimators Point Estimator what is the best single value that can be used to estimate a population parameter b Interval Estimator what is the best interval refer to a con dence inter val that contains the population estimate Tied to the notion of the con dence interval is the con dence coefficient 1 oz Where 001 g oz g 010 4 Properties of point estimators Unbiased average values of the estimated parameter equals the population parameter b Consistent Estimators from sample converge to the true value the sample size increases c Ef cient Estimator with smallest sampling variance 5 Univariate Analysis Estimating point estimator i For population mean gt 7 Margin of error gt 196 Standard error of the estimator or 32194 If a is unknown and n 2 30 one can substitute 8 for 0 ii For population proportion gt 13 E n Margin of error imamIE n 32196013 n estimated Recall up gt 5 and n gt 5 b Estimating interval estimator 37 Econ 2370 Spring 2000 O Donnell i leneral function two tail test Point estimator 3 gt1 Standard Error A Population mean When n gt 30 B Population proportion A 1 gr 7 p 9 71 ii leneral function left tail test onesided confidence interval Point estimator zQStandard Error iii General function right tail test onesided confidence interval Point estimator QStandard Error iv values of and 0 for given values of oz oz two tail 0 one tail Con dence 0010 258 233 990 0020 233 2055 980 0025 224 196 975 0050 196 1645 950 0100 1645 128 900 6 Bivariate Analysis This type of analysis works with two samples each drawn from different populations For this form of bivariate analysis the research question is Are the populations different Using the example from the textbook one would want to test if the average MCAT scores for biochemistry and biology majors are the same If there is no difference between these two populations biochemistry and biology students the difference in their population means m 12 would equal 0 This research question will be addressed briefly in this section and in more detail in Chapters 9 and 10 Right now we wish to deal with the point and interval estimates from the samples drawn from two populations There are two kinds of data sets used for bivariate analysis Data sets are not paired or data sets are independent from one another There is no relationship between the two parameters differenced eg MCAT scores for Biochemistry and Biology Majors 38 Econ 2370 Spring 2000 O Donnell b Data sets are paired eg there is a relationship between the two data sets Examples comparing the differences in gas mileage when a car is rst given one type and then another type of gasoline test scores of trainees before and after Viewing an instructional Video Properties of Sampling distribution of 771 52 not paired Mean and Standard error 2 2 a a SEza 71 72 x1 x m 722 Margin of Error 2 2 a a 32196 4 i m 7amp2 lon dence interval twotail 2 2 a a 711gi3923t155 Ji2 m 7amp2 i If sampled populations are normally distributed then the sampling distribu tion of 771 52 is normally distributed regardless of size ii If the sampled populations are not normally distributed then the sampling distribution of 51 52 is approximately normally distributed when m and m are large due to the Central Limit Theorem iii If a and 03 are unknown but both m and m are greater than or equal to 30 you can substitute the sample variances for the population variances lV Use 2 values found in section 5BiV on preVious page b Properties of Sampling distribution of 131 132 not paired Mean and Standard Error l39 z m 7amp2 lm 132 P1 112 P191 P292 SE Owl gag l W K 39 Econ 2370 Spring 2000 O Donnell Margin of Error i196 111191 P2Q 2 7quot 712 lon dence Interval twotail i The sampling distribution of 131 132 is approximately normally distributed when m and n2 are large due to the Central Limit Theorem ii m and n2 must be sufficiently large so that the sampling distribution of 13 132 can be approximated by a normal distribution mpgQO mpg and meg gt 5 iii Use 2 values found in section 5Biv c Properties of Sampling distribution of 771 52 paired Mean and Standard error H where a is the variance of the di 39erenced data and m m n Margin of Error B 196 L 71 Con dence interval twotail L711 L712 j 7 d Properties of Sampling distribution of 131 132 paired Will not be covered in this class 7 Choosing a sample size Choosing a sample size is an application of the point and interval estimation techniques Suppose you want to generate a sample such that the margin of error is equal to some value let s call it B You also want a sample such that 95 of repeated sampling will given you a margin of error less than or equal to B 40 Econ 2370 Spring 2000 O Donnell For univariate and bivariate analyses each margin of error function is a function of n Here is the case for the population mean univariate case B 32 194 IfI rearrange the function above one nds the function for computing the sample size ngt 22 If a is not known the sample standard deviation can be used or a value based on the range of the values divided by 4 In order to prepare a sample with a different degrees of con dence just replace the margin of error function with the con dence interval function two tail version Below is a table of the set of function one can use to determine the sample size B is equal to margin of error Analysis Estimator Minimum sample size Univariate 77 n 2 g202BQ I3 n 2 xiQWVBQ Bivariate not paired 51 772 n 2 g2w 03B2 131 132 n 2 xi201101 meg82 For the Bivariate functions m m n B is the acceptable margin of error If a is not known the sample standard deviation can be used or a value based on the range of the values divided by 4 41 Econ 2370 Spring 2000 O Donnell 12 Chapter 8 Large Sample Estimation Whenever we take a sample we do so with the idea of learning something about the population from which the sample is drawn Provided that the sample is drawn in an unbiased manner we believe that it may be taken representative of the parent population But representatives are not all equally authoritative Spokesmen even official spokesmen do not always tell a reliable tale and it is necessary in retelling a story secondhand from such a source that we indicate the degree of confidence which may be placed in what the spokesman has said Just the journalist tries to emphasize for his readers the difference between rumours and usually well informed sources so too the statistician has to attempt a similar thing liven large sample the problem is easily enough disposed of intuitively But when the samples are small we have to face not only the possibility of bias but also the fact that the average standard deviation or proportion found in the sample may differ be quite appreciably from the population parameters it is sought to estimate through the sample It is evident that there can be no possibility of finding a method of estimation which will guarantee us a close estimate under all conditions All we can hope for is a method which will be the best possible in the sense that it will have a high probability of being correct in the long run MJ Moroney Facts from Figures 1 Points covered in this chapter 01 Two approaches to estimate population parameters eg to estimate the mean and variance of the population for a normal distribution and the proportion for a binomial distribution when these values are unknown Properties of sound estimators lalculation of the margin of error and confidence intervals How to choose a sample size 2 Prior material used in this section a b C Standard error measurement 2 scores Tchebysheflquots Theorem and Empirical Rule 36

### 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."

#### "Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### 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.