Sample Design - Sample Size, Sampling Frame & Technique

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By Super Admin

Published on 23 May 2008

Three Component of Sample Design. Sample Size, Sampling Frame & Sampling Technique. Equation, example, math and problems of sample size.

Sample Design - Sample Size, Sampling Frame & Technique

Sample Design

There are Three Component of Sample Design

1. Sample Size

2. Sampling Frame

3. Sampling Technique

SAMPLE SIZE

* Large Population Size’s 1% to 2%.

* Medium Population Size’s 5% to 10%.

* Small Population Size’s 20% to 50%.

* If there is a budget & time constraint, a sample size of 30 items from each group irrespective of the total number of items of different groups may help objectively assess the characteristics of all the items belonging to different groups.

Determination of sample size through the approach based on confidence level and precision rate (if population size is unknown):

z^{2} x s^{2}^{}

n = --------

e^{2}

or

z^{2} x p x q

n = -----------^{} e2

where,

n = sample size

s = standard deviation

p = proportion of success for the indicator

q = 1 - p

z = standard normal variate at a given level of significance

(z = 1.96 at 95% level of confidence)

e = Precision rate or amount of admissible error in the estimate

If population size is known:

z^{2} x s^{2} . N

n = ---------------------

z^{2} x s^{2} + (N-1)e^{2}

or

z^{2} x p x q . N

n = ---------------------

z^{2} x p x q + (N-1)e^{2}

where,

n = sample size

p = proportion of success for the indicator

q = 1 - p

z = standard normal variate at a given level of significance

(z = 1.96 at 95% levels of confidence)

N= Population size

e = Precision rate or amount of admissible error in the estimate

The sample size will be adjusted further (if n> 5%N) using the formula given below:

n

n_{a}= ---------, where

1+n/N

n_{a}= adjusted sample size

PROBLEMS:

1. Determine the sample size for estimating the true weight of containers based on the following information:

i. Estimate must be made at 95% confidence level and within 0.15 kg of the true weight.

ii. The standard deviation of weight = 1.5 kg..

2. In an election for the post of President of the FBCCI there are 2 candidates: X and Y. You are interested in estimating the proportion of voters favoring Candidate X at 95% confidence interval and with an error not to exceed 2%. A previous poll showed 55% of the registered voters favoring candidate X. What sample size should be used for the purpose?

3. Beximco Pharma wishes to estimate the true proportion of defectiveness of its products at 99% confidence level and with 2% precision rate. Past record indicates that 6% of the products are defective. What would be the required sample size for estimating the true proportion of defectiveness in a production lot of 25000 units?

4. ACI wishes to estimate the true proportion of defectiveness of its products at 99% confidence level and with 3% precision rate. Past record indicates that 13% of the products are defective. What would be the required sample size for estimating the true proportion of defectiveness in a production lot of 8000 units?

5. The government wishes to be 95% certain of estimating the mean income of garments workers within an error of Tk. 20. Past studies indicate that the standard deviation of income is Tk. 200. What size of sample of garments workers should be used to obtain a reliable estimate of the mean income?

6. Monno Ceramic wishes to estimate the true proportion of defectiveness of its products at 99% confidence level and with 3% precision rate. Past record indicates that 9% of the products are defective. What would be the required sample size for estimating the true proportion of defectiveness in a production lot of 10000 units?

Sampling Frame

The List Containing the Particulars about all the items of a Population is known as the Sampling Frame. It is Prepared with a view to facilitating the Researcher to Select required Samples.

Sample Technique

Based on the Methods of Drawing Samples, Sampling Techniques are broadly be divided into two types:

(I) Random Sampling

(II) Non Random Sampling

Random Sampling

1. Simple Random Sampling

2. Stratified Random Sampling

3. Cluster Random Sampling

4. Systematic Random Sampling

5. Multiphase Random Sampling

6. Multistage Random Sampling

Nonrandom Sampling

1. Purposive /Judgmental

2. Convenience Sampling

3. Quota Sampling

There are Three Component of Sample Design

1. Sample Size

2. Sampling Frame

3. Sampling Technique

SAMPLE SIZE

* Large Population Size’s 1% to 2%.

* Medium Population Size’s 5% to 10%.

* Small Population Size’s 20% to 50%.

* If there is a budget & time constraint, a sample size of 30 items from each group irrespective of the total number of items of different groups may help objectively assess the characteristics of all the items belonging to different groups.

Determination of sample size through the approach based on confidence level and precision rate (if population size is unknown):

z

n = --------

e

or

z

n = -----------

where,

n = sample size

s = standard deviation

p = proportion of success for the indicator

q = 1 - p

z = standard normal variate at a given level of significance

(z = 1.96 at 95% level of confidence)

e = Precision rate or amount of admissible error in the estimate

If population size is known:

z

n = ---------------------

z

or

z

n = ---------------------

z

where,

n = sample size

p = proportion of success for the indicator

q = 1 - p

z = standard normal variate at a given level of significance

(z = 1.96 at 95% levels of confidence)

N= Population size

e = Precision rate or amount of admissible error in the estimate

The sample size will be adjusted further (if n> 5%N) using the formula given below:

n

n

1+n/N

n

PROBLEMS:

1. Determine the sample size for estimating the true weight of containers based on the following information:

i. Estimate must be made at 95% confidence level and within 0.15 kg of the true weight.

ii. The standard deviation of weight = 1.5 kg..

2. In an election for the post of President of the FBCCI there are 2 candidates: X and Y. You are interested in estimating the proportion of voters favoring Candidate X at 95% confidence interval and with an error not to exceed 2%. A previous poll showed 55% of the registered voters favoring candidate X. What sample size should be used for the purpose?

3. Beximco Pharma wishes to estimate the true proportion of defectiveness of its products at 99% confidence level and with 2% precision rate. Past record indicates that 6% of the products are defective. What would be the required sample size for estimating the true proportion of defectiveness in a production lot of 25000 units?

4. ACI wishes to estimate the true proportion of defectiveness of its products at 99% confidence level and with 3% precision rate. Past record indicates that 13% of the products are defective. What would be the required sample size for estimating the true proportion of defectiveness in a production lot of 8000 units?

5. The government wishes to be 95% certain of estimating the mean income of garments workers within an error of Tk. 20. Past studies indicate that the standard deviation of income is Tk. 200. What size of sample of garments workers should be used to obtain a reliable estimate of the mean income?

6. Monno Ceramic wishes to estimate the true proportion of defectiveness of its products at 99% confidence level and with 3% precision rate. Past record indicates that 9% of the products are defective. What would be the required sample size for estimating the true proportion of defectiveness in a production lot of 10000 units?

Sampling Frame

The List Containing the Particulars about all the items of a Population is known as the Sampling Frame. It is Prepared with a view to facilitating the Researcher to Select required Samples.

Sample Technique

Based on the Methods of Drawing Samples, Sampling Techniques are broadly be divided into two types:

(I) Random Sampling

(II) Non Random Sampling

Random Sampling

1. Simple Random Sampling

2. Stratified Random Sampling

3. Cluster Random Sampling

4. Systematic Random Sampling

5. Multiphase Random Sampling

6. Multistage Random Sampling

Nonrandom Sampling

1. Purposive /Judgmental

2. Convenience Sampling

3. Quota Sampling