# What is Sample size: Definition and 48 Discussions

Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power. In complicated studies there may be several different sample sizes: for example, in a stratified survey there would be different sizes for each stratum. In a census, data is sought for an entire population, hence the intended sample size is equal to the population. In experimental design, where a study may be divided into different treatment groups, there may be different sample sizes for each group.
Sample sizes may be chosen in several ways:

using experience – small samples, though sometimes unavoidable, can result in wide confidence intervals and risk of errors in statistical hypothesis testing.
using a target variance for an estimate to be derived from the sample eventually obtained, i.e. if a high precision is required (narrow confidence interval) this translates to a low target variance of the estimator.
using a target for the power of a statistical test to be applied once the sample is collected.
using a confidence level, i.e. the larger the required confidence level, the larger the sample size (given a constant precision requirement).

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1. ### I Is the Sample Size Calculation in This Article Accurate?

Hello! I will present an article tomorrow and I just found out the sample size calculation could be wrong (it's not my article). It's very urgent, if someone could help me to confirm if the sample size calculation is right or wrong (and if so, help me to calculate the correct amount) this would...
2. ### I Type 1 Error Increases with Sample Size?

My professor is teaching us that type 1 error increases with sample size if you keep alpha constant, and I think I understand what she's getting at, but I can't find anything online that supports the idea. Here's what I'm thinking: We accept that there is an equal chance that a flipped coin...
3. ### B Standard Deviation as Function of Sample Size

In high school, I was taught that the standard deviation drops as you increase the sample size. For this reason, larger sample sizes produce less fluctuation. At the time, I didn't question this because it made sense. Then, I was taught that the standard deviation does not drop as you increase...
4. ### A Sample Test | Component Lifetime

Hi, I'm currently working on a project for which I have to determine the Life-Time of a certain mechanical component within a certain confidence interval. By sampling a small number (let's say n = 10) of these components and measuring the number of hours until failure, I want to determine this...
5. ### I Standard Deviation Versus Sample Size & T-Distribution

I don't understand why does the standard deviation of a t-Distribution decreases as the degree of freedom (and, thus, also the sample size) increases when the sample standard deviation underestimates the population standard deviation?
6. ### How does one find sample size without a given variance?

Homework Statement "The mean pH value of a certain chemical is to be controlled at ##\mu = 5##. Deviation from this target value in either direction is to be detected with high probability. For this purpose it is proposed to measure a ceratin number of samples from each batch and decide that...
7. ### I Help with sample size to measure Form Error of a round metal part

Hello all First time on the Math side of this great Forum. I need to do a correlation study. There are 3 methods to measure Form Error of a round metal part. The base line is the traditional measuring method that is laborious but of the highest accuracy. A cnc machine measurement machine...
8. ### A Sample size required in hypergeometric test

I have a hypergeometric distribution with: N=total population of red and green balls, I now this K=total number of red balls, I don't know this n=sample size (number of investigated balls), I can choose this k=number of investigated balls that are red, I don't know this Red balls are a problem...
9. ### Determining a sample size

Homework Statement An investigator, interested in estimating a population mean, wants to be sure that the length of the 95% confidence interval does not exceed 5. What sample size should she use if σ = 18? The Attempt at a Solution the formula I found in my book is n = [(z_(α/2) σ)/E]^2...
10. ### Deducing Sample Size from Sample Proportion CI

Homework Statement Suppose we want to estimate a sample proportion to within 0.05 with 95% confidence, how large will the sample have to be? There is no other information about the distributions of the population or the sample. How do I approach this problem? Homework Equations See...
11. ### How to use DWT when sample size is smaller thn filter length

Hi, I am new member over here. I wanted to know how to perform discrete wavelet transform, probably using symmlet 8 wavelet with 16 Low/High pass filter coefficients using matrix transformation method when decomposing to a certain level the approximate coefficients i.e. sample size becomes less...
12. ### Weighted Mean: different sample size and variance

If I have three sets of numbers A is numbers between 0 and 0.09 B is numbers between 0.091 and 0.011 C is numbers between 0.011 and 0.1 where the number of elements in A are say, 37, B are 16 and C are 178. So the three arrays have different numbers of points and different distances, plotting...
13. ### Hypothesis testing, P-value, β-error, sample size for β<=0.1

Homework Statement The life in hours of a battery is known to be normally distributed, with standard deviation of 1.5 hours. A random sample of 12 batteries has a sample mean life time of 50 hours. a) Test the hypothesis that the mean battery life is 50.5 hours (by using α = 0.05). b) What is...
14. ### MHB Sample Size determination question

I have for class a research design of Nurse Practitioners, who have had clinical experience of 2 years or more with those, who have less than 1 year to determine if there is a difference in patient outcomes with those, who have diabetes and those, who have hypertension. IF I use an alpha level...
15. ### What is the updated version of FFT that does not require 2^n data points?

Back when I studied the FFT (many years ago), it was always described as transforming a sample based on 2^n data points. More recently, I have read that this restriction has been removed. Can anyone point me to a good reference on this newer form, preferably something available free on the 'net...
16. ### Finding sample size given info on confidence interval

Homework Statement Suppose that an investigator believes that virtually all values in the population are between 38 and 70. The appropriate sample size for estimating the true population mean within 2 units with 95% confidence level is approximately how much? Homework EquationsVariance of the...
17. ### Stuck on a sample size problem

I could do with some help here about a problem I had at work today. I have a process that dumps 8 parts in a bin every cycle. Each part is numbered, 1 to 8. (It is a big bin and it will contain an equal quantity of each number). I need to measure one part of each number, so I need to grab a...
18. ### Help with use of Chebyshev's inequality and sample size

Homework Statement Homework Equations P (|Y - μ| < kσ) ≥ 1 - Var(Y)/(k2σ2) = 1 - 1/k2 ?? The Attempt at a Solution using the equation above 1 - 1/k2 = .9 .1 = 1/k2 k2 = 10 k = √10 = 3.162 k = number of standard deviations. After this I don't know where to go...
19. ### Power calculations to get sample size needed to run an experiment

Hi everyone! I am writing a paper in development/experimental economics concerning how household bargaining power (i.e. how much say the husband and wife has about how to spend household income) affect how much money is spent on children. I am going to conduct an experiment and is now in the...
20. ### How do you estimate the sample size of a population given that there i

i need the formulas and the steps i know how to use the confidence interval equation after that it gets dark $$\frac{N*Var(x)}{(N-1)B^{2}/k^{2} + Var(x)}$$ break down the above equations into many steps and formulas
21. ### Assigning exponential weights depending upon sample size

I'm trying to find a function which will assign exponential weights depending upon sample size. nu=an equally space coefficient sequence (.05,..,.5; by=.05). m=sample size (10 in this case) Adding each observation in nu, implies a weight of 1, which makes the sum of weights m. I need...
22. ### Hi,I have the task to come up with a sample size for a new

Hi, I have the task to come up with a sample size for a new product, X. We manufacture 5 pieces a day of this product X and therefore has an yearly volume of 1300 pieces. Btw, we can manufacture only one product X at a time and hence its not done in batches. The reason behind this task is to...
23. ### Regression analysis sample size problem

Hi there, Could anybody offer any advice on a linear regression sample size problem? I am using regression to predict the energy consumption (watt/mile) of an electric car based on a number of parameters such as average velocity, max velocity, average acceleration, the number of stops...
24. ### Sample Size and Standard Deviation of the Sampling Distribution of the Mean

Hi, I am doing an undergraduate introductory statistics course and I'm trying to understand some basic concepts. I'm trying to understand why the sample size (n) affects the standard deviation of the sampling distribution of the mean (σ_{M}) I understand how a sample size affects the...
25. ### Effect of sample size when using periodic boundary conditions in 2D Ising model

Hi, I'm currently using the Monte Carlo Metropolis algorithm to investigate the 2D Ising model. I have an NxN lattice of points with periodic boundary conditions imposed. I was wondering if anyone could explain why the sharpness of the phase transition is affected by the size of N? I.e...
26. ### When does difference in sample size become an issue?

I was comparing two different groups, and in one, my n was 1600, and the other n was around 700. I found pretty much all significant differences, but is that maybe due to sample size. I tried doing a random selection making the sample sizes equal (both around 700) and got more or less the same...
27. ### Question about sum of primes and sample size

My question is this, is there a known convergence of the sum of primes divided by the square of the sample size? I've just been looking at it, admittedly with only the first 50,000 primes, and it looks as if it is converging on a number near 6. If you plot the points below, you might see what...
28. ### How to fine the required sample size

Homework Statement Given info: cost1=$4, σ1=10, W1=N1/N=0.4 cost2=$9, σ2=20, W2=N2/N=0.6 The second part: Find the sample size required, under this optimal allocation to make V(ybar) = 1. Ignore the finite population correction factor. Homework Equations The equation I used for...
29. ### Determine the required sample size of collection

Hi. Regarding bus inter-arrival times how to determine how much empirical data we must collect and how can we determine the required sample size from this collection in order to get a statistical significant representation? Regards
30. ### Most probable extreme value depending on sample size

Dear all, I have read that if the distribution of X belongs to the exponential family, then the maxima drawn from a sample of X follow: f(x) = \frac{1}{\beta} exp{(-\frac{x-\mu}{\beta} - exp{(-\frac{x-\mu}{\beta})})} in the limit of infinetely large sample. The above is apparently called...
31. ### Sample Size calculation, defect analysis

I am testing a change made to a software application; a function had to be rewritten to perform in a completely different way. The specific part of this application iterates through input data sets and outputs the data to another application. In order to test that data was being sent...
32. ### Statistics, sample size determination

Homework Statement Glucose level is normally distributed, standard deviation is known to be 25 units; determine the sample size needed to be 95% confident that the sample mean and the true population mean differ by at most 4 units. Homework Equations (work shown below) The Attempt...
33. ### How to calculate how big of a sample size is needed for the Central Limit Theorem?

Is there a way to calculate/estimate how big a sample from a parent distribution would need to be for the distribution of the mean of that sample to be approximately normally distributed?
34. ### Effect of Outlier on Confidence Interval Width

\begin{tabular}{lcr} 418 & 421 & 422 & 425& 427 & 431 \tabularnewline 434 & 437 & 439 & 446 & 447 & 448 & 453 \tabularnewline 454 & 463 & 465 \end{tabular} 1. Calc the sample mean and sample standard deviation. \sum_{i=1}^{17} x_i=7451 and \sum_{i=1}^{17} x_i^2=3269399 n=17...
35. ### Estimating group sample size

I'm working on this puzzle: The people in a country are partitioned into clans. In order to estimate the average size of a clan, a survey is conducted where 1000 randomly selected people are asked to state the size of the clan to which they belong. How does one compute an estimate average...
36. ### Finding a sample size that would give a certain probability of sucess

Homework Statement a population of n people contain k individuals with a disease. a sample of m people without replacement are chosen. how big should m be so that the probability of having at least one person with the disease is approximately .9? find m when n= 1000 and k= 10 hint...
37. ### Sample size without standard Deviation

Hello again, I have a question here that asks me to find how large a sample size is, but I have no Standard deviation. How would you tackle this> How large a sample size do we need to estimate the mean annual income of natives in New York, correct to within \$1000 with probability 0.99? No...
38. ### P-Chart: Diff. btwn lot & sample size

Hi need some clearance of idea: A process produces rubber belts in lots of sizes 2,500. Inspection records on the last 20 lots reveal the following data: then u have data in the format: Lot Number non-conforming belts 1 230 2 235...
39. ### Calculating Sample Size for an Olympic Sprinter Experiment

Dear forum pal, Here is my problem: - We would like to buid an experiment in order to check the effect of a new energy drink that is destined to the olympic sprinters (100m). - Here are our requirements for the experiment. - Type I error = alpha = less than 0.05 - Power = 1-beta =...
40. ### Calculating Standard Error for Sample Size: A Guide

hi, just wondering if there different ways to calculate the standard error for large and small sample size and if its so wats the formula we use? please give me a hand, hope this question makes sense. cheers
41. ### Determining Sample Size for Conversion to Ag2S

Sometimes, when repeated assays are to be performed, the sample size is standardized and chosen such that the ultimately measured quantigy is numerically equivalent to some other desired proportionate quantity. suppose the sulfur content of a mineral sample is determined by complete...
42. ### Determining sample size needed to test hypothesis

This is a statistics and probability question. I've been trying to figure this out for hours but I'm getting nowhere: I have to test the hypothesis that the true average value of a sample is 6.2. I will reject the null hypothesis if with 95% confidence if the true average value is indeed 6.2...
43. ### Determining sample size needed to test hypothesis

I always do questions on school that ask for a test of hypothesis where the sample data is already give, but what if you want to do it the other way around, by first figuring out what sample size is needed to test a hypothesis at a given accuracy. Is that possible?
44. ### Calculating the PMF of Min. Observation of Discrete Distribution Sample Size 5

Hi, I know this isn't hard, but I have a block on it. Here's the question: Let f(x)=1/6, x=1,2,3,4,5,6 zero elsewhere be the pmf of a distribution of the discrete type. Show that the pmf of the smallest observation of a random sample of size 5 from this distribution is...
45. ### Statistics: sample median, means, s.d. vs sample size

i have a set containing 10000 data. i took 1000 samples of size 4, 16, 64, and 1024 and took the medians, means, and stadard deviations of each size. i graphed them sd of medians vs sample size, sd of mean vs sample size, and sd of s.d. vs sample size. for sample mean, i know from a textbook...
46. ### Sample size, probability

In a set of 400 hats, each hat is represented by one of six colors (brown, pink, red, orange, blue, yellow). You may assume that each color is represented rather equally in the 400 hats. What is the minimum amount of samples we must take to be likely to have a sample which has a hat of every...
47. ### Sample size needed for power of a study

I can't remember how to figure out this type of problem. I swear I figured this out once before, but now I am clueless.. Let's say there's a certain achievement test and you know that 5th graders in general score a mean of 200 on the test. The known standard deviation of the population is 48...
48. ### Seeking Help with Stats: Sample Size Guidance Needed

Hi! I'm new to this forum. I took some stats in University but that was so long ago that I don't remember much. I'm trying to figure out how big of a sample size I need to generate some stats for the company I work for. I'm not sure what info is needed but if anyone is interested in helping...