Present the formula for an SRSWOR of n UC students by using the same data to find the estimate of the mean GPA for N students in the UC 2022 cohort.

Stat 130. Fall 2022
Homework- 6, Total Points = 10
Due on Saturday, November 5, 2022, before 5:00 PM
Write Your Name at the top right corner of the first page.
turn in your work on Canvas.
Homework-6 questions are from the Chapter 3, Sections 3.1, 3.2, and 3.4.1 materials of Lohr, and the lectures on October 26, 28, and 31, and November 2.
Points = 1 + 2 + 2 + 2 + 3 = 10.
For a stratified random sampling of size 10,000 from the 2022 cohort of UC Freshman Students using the proportional allocation, the sample sizes (nh) and the population sizes (Nh) for the stratum h (h = 1, … , 9) are given below.
h Stratum Nh Nh/N = nh/n nh
1 UCB 14603 0.0600 600
2 UCD 35563 0.1462 1462
3 UCI 25023 0.1029 1029
4 UCLA 12825 0.0527 527
5 UCM 27046 0.1112 1112
6 UCR 37262 0.1532 1532
7 UCSD 31160 0.1281 1281
8 UCSB 28701 0.1180 1180
9 UCSC 31075 0.1277 1277
Total N = 243258 1.0000 n =
10000
Let yhi , i= 1, … , nh, h = 1, … , 9, be the 2022 fall quarter GPA of students selected in the stratified random sample, where an SRSWOR of size nh is drawn from the hth stratum.
(a) Points = 1.
Present the formula to find the estimate of the hth stratum mean GPA for Nh students.
(b) Points = 2.
Present the formula for the stratified random sample to find the estimate of the mean GPA for N students in the
UC 2022 cohort.
(c) Points = 2.
Present the formula for an SRSWOR of n UC students by using the same data to find the estimate of the mean GPA for N students in the UC 2022 cohort.
(d) Points = 2.
Compare the formulas in (b) and (c) for the proportional allocation by taking the difference between them.
Clearly write your findings.
(e) Points = (2 + 1) = 3.
Present the formulas of standard errors for two estimates in (b) and (c) and compare them. Clearly present your findings.

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