Question: Question #3 (both 454 & 854 - 10 points): We saw in class how to use SAS to compute y and under SRS and

Question #3 (both 454 & 854 - 10 points): We saw in class how to use SAS to compute y and under SRS and STSRS. We also saw how to use use SAS to compute VSRS (A), VSRS(A), VSTSRS(A) and VSTSRS (A). However, SAS must be able to compute and A, as well as their corresponding variance estimators, under more sampling designs that just SRS and STSRS. Hence, SURVEYMEANS uses more general formulas than the ones given in class. However, these more general formulas simplify to the ones given in class, and this question is concerned with proving this. SAS must also be able to perform calculations under two-stage or cluster sampling, something that we will discuss later in STAT 454/854. Looking at the online help for SURVEYMEANS, the general formulas for YSAS and tsas (and their corresponding variance estimators) involve triple sums. In the context of this question, these triple sum formulas simplify to the following. The SAS formula for estimating a population mean yu is given by H nh 1 YSAS W.. whi Whi h=1 i=1 where The variances estimator of SAS is given by where W.. = H VSAS(SAS) = h=1 H nh - h=1 i=1 Whi - nh(1 nh/Nh) nh-1 nh i=1 (Chi - h.) nh 1 Whi Chi (Yhi - YSAS) and Ch. nh IM Chi i=1 W.. The SAS formula for estimating a population total tu is given by H nh tsas = wnt Whi The variances estimator of tsAs is given by h=1 i=1 where H VSAS (SAS) = h=1 nh(1 nh/Nh) nh-1 nh (em - elia)2 i=1 nh 1 eni = Whi Yhi and ehi nh Using the above formulas and the ones given in class show that: (a) SAS simplifies to is under SRS Assign #1 STAT 454/854 (W2024) (b) VSAS(SAS) simplifies to srs(s) under SRS (c) SAS simplifies to under STSRS (d) VSAS(SAS) simplifies to VSTSRS() under STSRS (e) tsas simplifies to = Nys under SRS (f) VSAs (sas) simplifies to VSRS (t) under SRS (g) tsas simplifies to under STSRS (h) Vsas (sas) simplifies to VSTSRS (^) under STSRS. i=1 3 of 8

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Outdoor Adventures Inc. is in a highly seasonal business, and the following summary balance sheet data show its assets and liabilities at peak and off- peak seasons (in thousands of dollars): Peak...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

For monotone functions f, f0: P Q between posets (P, vP ) and (Q, vQ), let f v f(i) Prove that the binary relation v is a partial order. [3 marks] (ii) For monotone functions between posets p : P 0...

A UK company has a trading loss of 50,000 for the year to 31 March 2021. During the year, the company receives overseas property income (net of 40% withholding tax) of 12,000. Show the corporation...

Obtain the area under the standard normal curve a. To the right of z = 1.43 b. To the left of z = 1.65 c. To the right of z = .65 d. To the left of z = .89

On the foreign exchange market, who demands dollarsU.S. investors or foreign investors? Why does an increase in U.S. interest rates relative to Japanese interest rates increase the demand for...

3. Using one of the programs you identified in the first exercise, develop a mock application. (Applications can often be downloaded. If not, choose a similar program that does have a downloadable...

The University of Danville is a private not-for-profit university that starts the current year with $700,000 in net assets: $400,000 unrestricted, $200,000 temporarily restricted, and $100,000...

Need help with the following question. Thank you The following information is for Skysong Day Real Estate: $ 60700 Cash Prepaid Insurance Skysong Day Real Estate Balance Sheet December 31, 2018 $...

After the success of the company's first two months, Santana Rey continues to operate Business Solutions. The November 30, 2021, unadjusted trial balance of Business Solutions (reflecting its...

A couple thinking about retirement decide to put aside $3,000 each year in a savings plan that earns 8% interest. In 5 years they will receive a gift of $10,000 that also can be invested. a. How much...

Matrix Inc performs following job and it wants you to compute Actual Costing and Nominal Costing Based on following info:

Question 18 2 Points As a result of continuously measuring and evaluating their performance, Dana Pastries identified five areas that require improvement. Accordingly, they launched a new initiative...

Debate the following statement: 'Big Data' and the buzz of the so-called 'green marketing' and 'sustainable marketing' are being used nowadays by marketing professionals to increase the grip and the...

Required neat and clear handwritten solution with all steps. Knowing that a = 0.14 m, b = 0.54 m, c= 0.35 m and F = 3.6 kN, determine the magnitude of the force at point B. A B F KN C D bm am bm EO cm

Write a MATLAB script to visualize a 3 D plot of a parametric surface representing a spherical spiral. The parametric equations for a spherical spiral are given by: x ( ? , \ theta ) = Rsin ( ? ) cos...

Candlewood LLC started business on September 1, and it adopted a calendar tax year. During the year, Candlewood incurred $6,500 in legal fees for drafting the LLC's operating agreement and $3,000 in...

7 A 29-year-old, previously healthy man suddenly collapses at a party where legal and illicit drugs are being used. Enroute to the hospital, he requires resuscitation with defibrillation to establish...

The accompanying MINITAB output resulted from applying both the backward elimination method and the forward selection method to the wood specific gravity data referred to in Exercise 56. For each...

Multiple regression output from MINITAB for the PAH data of Exercise 53 in the previous section included the following information: Unusual Observations Obs x1 flth Fit SE Fit Residual St Resid 6...

Refer to the water-discharge data given in Exercise 55 and let y ln(q), x1 ln(a), and x2 ln(b). Consider fitting the model Y 0 1x1 2x2 !. a. The resulting hiis are .138, .302, .266, .604, .464,...