I shall collect data from a population in order to estimate population parameters (e.g. and 2) by using estimating techniques.

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SURVEYING THE ISSUES.

INTRODUCTION:

I shall collect data from a population in order to estimate population parameters

(e.g. μ and σ2) by using estimating techniques.

I shall take a random sample as well as calculating and comparing confidence intervals.  

AIM:

I’m going to undertake a small-scale survey using a questionnaire, to estimate population parameters.

POPULATIONS USED:

I’m going to take the number of 13 to 16 year old students at Newmarket Upper School who took part in the questionnaire as my population as my first population and the number of 13 to 16 year olds in Suffolk as my second population.

SAMPLE SIZE:

To get my sample from the population, I will use a random number generator to get n responses from the question. This would be the sample for my first population:

To make accurate estimates of population parameters the sample must be large enough.

The Central Limit Theorem allows predictions to be made about the distribution of the sample mean without any knowledge of the distribution of the parent population, as long as the sample is large enough.

For this reason, my sample size, n  will be set at 100, which I consider large enough for the distribution of its mean to be Normal. (According to the Central Limit Theorem).

THE STATISTICAL THEORY

Central Limit Theorem:

  1. If the sample size is large enough, the distribution of the sample mean is approximately Normal.
  2. The variance of the distribution of the sample mean is equal to the variance of the sample mean divided by the sample size; σ2

                                                  n                                            

                                                                       _

Symbolically if X~ (unknown)(μ, σ2) then   X n ~N   μ, σ 2 

                                                                                         n        

These approximations get closer as the sample size, n gets bigger.

(a good rule of thumb is n ≥ 30)


 HOW DATA WAS COLLECTED:

374 students (male and female aged between 13 and 16 years old.) undertook a small-scale survey on matters such as the amount of pocket money they get on weekly basis, time spent on watching T.V. and part time jobs.

For my question “How much pocket money do you normally get on weekly basis?” I recorded all the response I got as shown in the table below.

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Row data.



WHAT CALCULATIONS WILL BE MADE USING THE DATA.

  1. The mean, standard deviation and variance of the sample.

  1. These will be used to estimate the variance and standard deviation of the parent population.

  1. This will also be used to create confidence intervals for the mean of the parent population.

  1. Also, calculations that determine the size that a possible sample could be to achieve a certain percentage confidence interval for the mean to be a certain range.

First I have to sort all the responses I got ...

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