数学代写|MTH432 Sampling theory

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MTH432课程简介

Syllabus : Principles of sample surveys; Simple, stratified and unequal probability sampling with and without replacement; ratio, product and regression method of estimation, Varying Probability Scheme

An overview of probability and statistics. Experiments; sample spaces; random variables; probability measures and distributions; combinatorics; expectation; data collection and analysis; confidence intervals; selected hypothesis tests.
Lecture
Credits: 3
Prerequisite: MTH 232
Offered in Fall Semester

Prerequisites 

Books: You can choose any one of the following book for your reference. Books at serial numbers 1 and 2 are easily available, so I will base my lectures on them. Other books are available in the library.

Sampling Techniques : W.G. Cochran, Wiley (Low price edition available)

Theory and Methods of Survey Sampling : Parimal Mukhopadhyay, Prentice Hall of India

Theory of Sample surveys with applications : P.V. Sukhatme, B.V Sukhatme, S. Sukhatme and C. Asok, IASRI, Delhi

Sampling Methodologies and Applications : P.S.R.S. Rao, Chapman and Hall/ CRC

Sampling Theory and Methods : M.N. Murthy, Statistical Publishing Society, Calcutta (Out of print)

Elements of sampling theory and methods : Z. Govindrajalu, Prentice Hall

Sampling Methods- Exercises and Solutions : Pascal Ardilly and Yves Tille’ (Download here through IITK Library link)

MTH432 Sampling theory HELP（EXAM HELP， ONLINE TUTOR）

Based on the given information, we can infer the following:

• The population is divided into five strata, with stratum sizes given by $N = (3529, 4775, 4257, 4077, 3026)$.
• Proportional allocation is used to sample from each stratum, with sample sizes given by $n = (36, 49, 43, 41, 31)$.
• Two variables are of interest: price and the proportion of products with age less than or equal to 11 years old.
• For each variable, the table provides estimates of the sample mean and proportion, along with 95% confidence intervals and the standard error of the estimate.

For the variable of price, the estimate of the population mean is $\hat{\mu}{y,\cdot} = 9.3861$, with a 95% confidence interval of $(8.6759, 10.0964)$, and a standard error of $SE(\hat{\mu}{y,\cdot}) = 0.3624$. This means that we are 95% confident that the true population mean price is between 8.6759 and 10.0964, based on the sample mean of 9.3861.

For the variable of proportion of products with age less than or equal to 11 years old, the estimate of the population proportion is $\hat{p}{y,\cdot} = 0.3755$, with a 95% confidence interval of $(0.3086, 0.4424)$, and a standard error of $SE(\hat{p}{y,\cdot}) = 0.0341$. This means that we are 95% confident that the true population proportion of products with age less than or equal to 11 years old is between 0.3086 and 0.4424, based on the sample proportion of 0.3755.

Based on the given information, we can infer the following:

• A simple random sample (SRS) of size $n=200$ was taken from the population.
• Two variables are of interest: price and the proportion of products with age less than or equal to 11 years old.
• For each variable, the table provides estimates of the sample mean and proportion, along with 95% confidence intervals and the standard error of the estimate.

For the variable of price, the estimate of the population mean is $\hat{\mu}{y,\cdot} = 9.9250$, with a 95% confidence interval of $(8.9761, 10.8739)$, and a standard error of $SE(\hat{\mu}{y,\cdot}) = 0.4841$. This means that we are 95% confident that the true population mean price is between 8.9761 and 10.8739, based on the sample mean of 9.9250.

For the variable of proportion of products with age less than or equal to 11 years old, the estimate of the population proportion is $\hat{p}{y,\cdot} = 0.3600$, with a 95% confidence interval of $(0.2936, 0.4264)$, and a standard error of $SE(\hat{p}{y,\cdot}) = 0.0339$. This means that we are 95% confident that the true population proportion of products with age less than or equal to 11 years old is between 0.2936 and 0.4264, based on the sample proportion of 0.3600.

The table also notes that the standard error for the mean is larger than the standard error for the proportion. This is because the variable of price is related to the stratification variable, which means that stratification can have an effect on the variability of the variable. However, the variable of proportion of products with age less than or equal to 11 years old is not related to the stratification variable, so stratification does not have an effect on the variability of that variable.

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