Search
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.

# Sample size calculation - Math Problem Example

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…

## Extract of sampleSample size calculation

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 ... Read 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)
https://studentshare.net/education/308075-sample-size-calculation.
“Sample Size Calculation Math Problem Example | Topics and Well Written Essays - 2250 Words”, n.d. https://studentshare.net/education/308075-sample-size-calculation.
Click to create a comment
CHECK THESE SAMPLES - THEY ALSO FIT YOUR TOPIC
Soil Mechanics Exercises
So, this is a well graded soil. (b) As Plasticity index Ip = liquid limit – plastic limit So Ip of soft sandy clay= 36 – 15 = 21 Ip of Firm silty clay = 47 - 18 = 29 Ip of Stiff Clay = 67 – 19 = 48 And Liquidity Index IL = So IL of soft sand clay = 27-15/21 = 0.57 IL of Firm silty clay = 29-18/29 = 0.38 IL of Stiff clay = 25-19/48 = 0.125 Question No.
10 Pages(2500 words)Math Problem
Structures, Fluid Mechanics, Materials, and Soil Mechanics

Prestressing is normally accomplished in 3 ways which are: pre-tensioned concrete, followed by bonded and the unbonded and post-tensioned concrete.Pre-tensioned concrete is then cast all around the already tensioned tendons. The pickled concrete sticks to and also ties itself with the bars.

11 Pages(2500 words)Math Problem
The technique revolves around five (5) simple steps. These steps are: i. Setting up a probability distribution for each of the three variable – material cost, labor cost and utilities cost ii. Preparing a cumulative probability distribution for each of the three variables iii.
16 Pages(4000 words)Math Problem
HW
2. Report a 95% confidence interval for this difference. The 95% CI for this difference ranges from -2.98 to -1.22 3. Write a sentence interpreting both the unadjusted mean difference and the corresponding confidence interval. When not considering other variables, women in 1985 earned approximately 2.1 dollars less than the men did; and 95% of the times, the actual values for this estimate would fall between 2.98 dollars to 1.22 dollars less then what the men earned on an average.
4 Pages(1000 words)Math Problem
This is a significant area of mathematics that creates meaning from data to enable people draw conclusions. Statistics is applicable in a number of fields, including agriculture, education, military, medicine, gambling, just to mention a few. Sometimes statistical interpretations can mislead people on the characteristics of data due to insufficient information or lack of information altogether.
3 Pages(750 words)Math Problem
Assignment
The inferential statistics helps a researcher to conclude beyond the descriptive conclusions of data. There are various quantitative data analysis methods that help in testing the quantitative model. The inferential statistical techniques correlation or bivariate regression analysis are used for examining relationship between two continuous variables (one independent variable and one dependent variable).
4 Pages(1000 words)Math Problem
Statistical Methods
The confidence interval is the result from the test statistic N (0, 1). Test statistic: Under H0, tn - 2 distribution where a is the sample slope parameter, A is the population slope parameter, s is the sample estimate for the standard deviation. The results from Q4 are a = 0.0867, s = 1.4495 and Cxx = 267.6 and A = 0.
8 Pages(2000 words)Math Problem
Discussion Paper Sample Size Statistical Analysis
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 particular method of sampling used and are specified in later sections, when each sampling method is described in turn.
2 Pages(500 words)Essay
'Level of processing' model of memory
Thus, for example, if you tried to memorize a list of key revision words, repeating each word to yourself (a low level of processing), this would lead to poorer recall than if you tried to associate each key word with another word or a picture or a sound.
3 Pages(750 words)Math Problem
Maths Report
A car with an engine size less than 1.8L considered as the small engine size car and a car with an engine size greater or equal to 1.8L considered as the bigger engine size cars. The results indicated that there is a strong negative linear
4 Pages(1000 words)Math Problem
Let us find you another Math Problem on topic Sample size calculation for FREE!
+16312120006