Nobody downloaded yet

Sample size calculation - Math Problem Example

Comments (0) Cite this document
Summary
Sampling is an important issue when undertaking research, there are various methods of sampling that can be used and the sampling method must be specifies in any study, the reason for specifying the sampling method is because this helps validate the sample used…
Download full paperFile format: .doc, available for editing
GRAB THE BEST PAPER94.8% of users find it useful
Sample size calculation
Read TextPreview

Extract of sample "Sample size calculation"

Download file to see previous pages Sampling is important in that we involve fewer respondents than using the entire population, the sample saves time and money and an appropriate sample will represent the population in that the results derived from the sample will explain the population with less error. A large sample will waste time and money while a small sample will give inaccurate results.
In any given study if we were to determine the mean of the population and the mean of the sample there means are not the same, the difference between the two is termed as an error, therefore when determining the sample size we need to consider the expected error that will result to these differences. The other factor to consider is the margin of this error, this represents the maximum possible difference between the sample mean and the population mean. We consider also consider the standard deviation of the population, the reason why we consider the standard deviation is because we assume that the population assumes a normal distribution which is depicted by the central limit theorem that states that as the number of variables increase indefinitely then the variables assumes a normal distribution.
For a clustered study there is need to consider the sampling design when calculating the sample size, we consider the number of clusters after calculating the sample size, after determining the sample size as shown above we multiply the results by the number of clusters, the results of this are then mu...
n = [(1.96/2 . 6.9) /(0.4)] 2
n = 285.779
In this case therefore we will use a sample size n =286 derived from rounding off the figure into the nearest whole number.
Cluster sampling:
For a clustered study there is need to consider the sampling design when calculating the sample size, we consider the number of clusters after calculating the sample size, after determining the sample size as shown above we multiply the results by the number of clusters, the results of this are then multiplied by the an expected non response or error, example use 5%. After multiplying we then divide the results by the number of clusters to determine the number of n in each cluster.
Example assumes that we have 10 clusters and we assume the level of error is 5% from our above results; the following will be the results:
285.779 X 10 = 2857.79
2857.79 X 1.05 = 3000.68
We will consider a 3,000 sample size and for each cluster we will have n = 300
Formula 2:
The other formula that can be used is where we have the prevalence of the variable being studies, in this case for example we have a prevalence rate of 40% of a disease and we use the following formula:
n = [Z2. x (1-x)]/ E2
Where Z is the confidence interval where if we choose 95% the area under the normal curve will be 1.96
E is the expected margin error and x is the expected prevalence of the variable being studied.
Formula 3:
Cochran (1963) formulated a formula that could be used in the calculation of the sample size in a study, the formula is as follows:
n = (Z2 PQ)/ e2
Where n is the sample size, Z is the confidence interval, P is the estimated proportion of the attribute under study, q is derived from 1 - p and finally e is the precision level.
He further stated that the above sample would further be ...Download file to see next pagesRead More
Cite this document
  • APA
  • MLA
  • CHICAGO
(“Sample size calculation Math Problem Example | Topics and Well Written Essays - 2250 words”, n.d.)
Sample size calculation Math Problem Example | Topics and Well Written Essays - 2250 words. Retrieved from https://studentshare.org/education/1531490-sample-size-calculation
(Sample Size Calculation Math Problem Example | Topics and Well Written Essays - 2250 Words)
Sample Size Calculation Math Problem Example | Topics and Well Written Essays - 2250 Words. https://studentshare.org/education/1531490-sample-size-calculation.
“Sample Size Calculation Math Problem Example | Topics and Well Written Essays - 2250 Words”, n.d. https://studentshare.org/education/1531490-sample-size-calculation.
  • Cited: 0 times
Comments (0)
Click to create a comment or rate a document

CHECK THESE SAMPLES OF Sample size calculation

Sampling Strategy and Sample size for a Quantatitive Research Plan

...?Sampling Strategy and Sample size for a Quantitative Research Plan Introduction In consideration of the research question at hand, it is observed that the study should use a quantitative approach. Specifically, a cross-sectional study will be used. In this research plan, data is collected on the whole study population, or at least a sub-set of the population, at a single point in time to examine the relationship between the dependent variable and other variables of interest (Ismail et al, 2011). The research questions for this study are the following: 1. To what extent does leadership effectiveness affect workers task performance? 2. What is the relationship between effective leadership...
3 Pages(750 words)Research Paper

Hewlett-Punning Case: Questionnaire Design Sampling and Sample Size

.... It is therefore expensive and cumbersome to conduct a whole population census sampling (Yates, 1960). The Random sampling design shall entail calling any number at random without bias and seeking for permission to carry out the survey. Once the respondent grants permission, the researcher carries on and asks the set questionnaire questions in search of answers. The design makes it possible for the research to calculate the sampling error. A standard deviation of $45 is quite large, and, in turn, getting it requires a relatively large sample size. The management of the restaurant was out to get a very high degree of accuracy, and in that...
3 Pages(750 words)Case Study

Sample

...Harris Kamran English Literature 14 December 2007 Rhetorical Modes In his book Healing Together: How to Bring Peace into Your Life and the World, Lee Jampolsky deals with the subject of personal problems, sufferings and crisis, how they affect our lives and what is the best way to deal with them in order to gain the most benefits from the troubling situations. There are many rhetorical modes, and each mode has certain reasons to be used in a composition, and hence, produces a certain affect due to which the writer chooses to use that particular mode. It is also common for writers to use a variety of modes, instead of just one... Kamran English...
2 Pages(500 words)Essay

Discussion Paper Sample Size Statistical Analysis

...Discussion Paper "Sample Size" Statistical Analysis The article under analysis discusses the problems of sample size determination and proposes practical guidelines for hypothesis testing. The author of the article states that the information gathered from a sample (i.e. measurements, facts and/or opinions) will normally give a good indication of the measurements, facts and/or opinions of the population from which it was drawn. The advantages of sampling are usually smaller costs, time and resources. A general disadvantage is a natural resistance by the layman in accepting the results as representative. Other disadvantages depend on the...
2 Pages(500 words)Essay

Calculation

...Management Accounting What is the contribution margin per unit for a box of peanut fudge What is the contribution margin ratio A. Contribution Margin = Selling Price - Direct Cost Brittle, Inc.'s direct costs are: Peanuts $0.70 Sugar $0.35 Butter $1.85 Other ingredients $0.34 Box, packing material $0.76 Selling commission $0.20 Total Direct Costs = $0.70 + $0.35 + $1.85 + $0.34 + $0.76 + $0.20 = $4.2 Contribution Margin = $5.60 - $4.2 = $1.40 B. Contribution Margin Ratio = Contribution Margin/Selling Price =$1.40/$5.60 = 0.25 2. How many boxes must be sold to break even What is the break-even sales revenue Fixed Costs = Fixed Overhead + Fixed Selling and Administrative Costs = $32, 300 + $12... Accounting ...
2 Pages(500 words)Essay

Sampling Strategy and Sample Size for a Quantitative Research Plan

...Sampling Strategy and Sample Size for a Quantitative Research Plan Population as used in this context refers to all people who have some degree of probability of becoming part of the sample size (Danielle, 2009). This means that they are also people who have some degree of becoming part of the respondents and thus are likely to interact directly with the researcher. For the given study where the researcher is seeking to identify the impact or effect of a 2-tier curriculum on the learning outcome of students, the population to be used would be identified to be students from one faculty of a designated university. Given the average enrolment of the...
6 Pages(1500 words)Coursework

Sampling Strategy and Sample Size for a Quantitative Research Plan

...Sampling Strategy for a Quantitative Research Plan Sampling Strategy for a Quantitative Research Plan Quantitative analysis is extremely valuable to the field of social sciences because it enables the researcher to accurately gauge the quality, reliability and validity of their findings. In order for this to occur effectively, however, the researcher must take care with the sample size and population that is chosen in order to get a truly representative sample that leads to solid, scientific conclusions. The first step toward ensuring that this happens is to develop a sound sampling strategy for the quantitative research plan. When considering how to set about this type of study, the researcher should consider the sampling size... will...
3 Pages(750 words)Research Paper

8_Sampling Strategy and Sample Size for a Qualitative Research Plan

...Recommending and justifying a sampling strategy and sample size the qualitative research plan Grade (April 24th, 2014) Recommending and justifying a sampling strategy and sample size the qualitative research plan The purposive sampling strategy under the non-probability sampling method is recommended for this study. The choice of the purposive sampling strategy is informed by the fact that, the study applies a qualitative research design, while the tool for collecting data applicable in the study is interviewing. In this respect, the target population for the study is well cut out and...
4 Pages(1000 words)Research Paper

Calculation

...= Investment Required to purchase the ATM- Amount Received by Selling Old ATM (1-Marginal Tax Rate) The bank will receive the current market price by selling old ATM machine, which is $200,000. The amount received is subject to marginal tax rate of 40%. Therefore, the amount received from selling the old ATM machine is reduced by 40%. On the other hand the gross outflow required for the installation of new ATM machine is $1,000,000. Therefore, the after tax selling price of the old ATM machine will be subtracted from the price paid for new ATM machine. The calculations are...
4 Pages(1000 words)Assignment

Sampling size and sample size for qualitative research

...Sampling Strategy and Sample Size al Affiliation: Sampling Strategy It’s generally impossible to study an entire population. As a result, a research relies heavily on sampling in order to acquire a section of population that will represent the rest of the population under study. In order for my study to achieve the set objective, stratified random sampling will be used. This is because the population is heterogeneous and has different groups, with some being related to the topic under study. Therefore, the use of this strategy will be significant in ensuring that there is a high degree of representativeness of all strata or layers in the...
5 Pages(1250 words)Coursework
sponsored ads
We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.

Let us find you another Math Problem on topic Sample size calculation for FREE!

Contact Us