Which Of The Following Are Not Required To Determine Sample Size Using The Sample Means Formula?

Contents:

What is a Sample Size?
How to Discover a Sample size:
- Role One: General Tips.
- Cochran's Sample Size Formula
- Yamane's Sample Size Formula
- Known Confidence Interval and Width (unknown population standard deviation).
- Known Confidence Interval and Width (known population standard deviation).
- Find a sample size to estimate a population mean
- Use Excel to detect a sample size.

Watch the video for an overview of how to find a sample size:

How to Find a Sample Size

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What is a "Sample Size"?

A sample size is a part of the population chosen for a survey or experiment. For case, yous might take a survey of dog owner's brand preferences. You won't want to survey all the millions of dog owners in the country (either considering it's besides expensive or time consuming), so you take a sample size. That may be several thousand owners. The sample size is a representation of all dog owner's brand preferences. If y'all choose your sample wisely, it volition be a proficient representation.

When Error can Creep in

When you simply survey a modest sample of the population, uncertainty creeps in to your statistics. If you can simply survey a certain percent of the true population, you can never be 100% certain that your statistics are a complete and accurate representation of the population. This uncertainty is called sampling error and is usually measured by a confidence interval. For case, you might state that your results are at a ninety% confidence level. That means if you were to repeat your survey over and over, 90% of the time your would get the same results.

A census is where every member of a population is surveyed, not just a sample.

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How to Find a Sample Size in Statistics

A sample is a percentage of the total population in statistics. You tin utilise the information from a sample to brand inferences almost a population equally a whole. For example, the standard deviation of a sample can exist used to estimate the standard deviation of a population. Finding a sample size tin can be one of the nearly challenging tasks in statistics and depends upon many factors including the size of your original population.

General Tips

Stride ane: Conduct a census if you have a small population. A "small" population volition depend on your upkeep and time constraints. For case, information technology may take a day to take a demography of a pupil torso at a pocket-sized private university of 1,000 students merely y'all may non have the time to survey 10,000 students at a large state university.

Step 2: Use a sample size from a similar study. Chances are, your type of study has already been undertaken by someone else. You'll need access to academic databases to search for a study (normally your school or college volition have access). A pitfall: you'll be relying on someone else correctly calculating the sample size. Any errors they have made in their calculations will transfer over to your study.

Step 3: Employ a table to find your sample size. If you take a adequately generic study, and then there is probably a table for information technology. For instance, if you have a clinical study, yous may be able to use a tabular array published in Machin et. al's Sample Size Tables for Clinical Studies, Third Edition.

Step iv: Use a sample size calculator. Various calculators are available online, some elementary, some more than complex and specialized. For case, this calculator is for group- or cluster-randomized trials (GRTs).

Pace 5: Use a formula. In that location are many dissimilar formulas you can use, depending on what you know (or don't know) about your population. If you know some parameters about your population (like a known standard deviation), you tin utilize the techniques below. If yous don't know much about your population, employ Slovin's formula..
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Cochran'south Sample Size Formula

Watch the video for an case:

Cochran's Formula for Sample Size

Can't encounter the video? Click here.

The Cochran formula allows you to calculate an ideal sample size given a desired level of precision, desired confidence level, and the estimated proportion of the attribute present in the population.

Cochran's formula is considered specially advisable in situations with big populations. A sample of whatever given size provides more information about a smaller population than a larger 1, then at that place'south a 'correction' through which the number given by Cochran'south formula can exist reduced if the whole population is relatively small.

The Cochran formula is:

Where:

eastward is the desired level of precision (i.east. the margin of error),
p is the (estimated) proportion of the population which has the attribute in question,
q is ane – p.

The z-value is constitute in a Z table.

Cochran's Formula Example

Suppose we are doing a study on the inhabitants of a large town, and want to find out how many households serve breakfast in the mornings. We don't have much data on the subject field to begin with, so we're going to assume that half of the families serve breakfast: this gives us maximum variability. So p = 0.5. At present let'southward say we want 95% confidence, and at to the lowest degree 5 percent—plus or minus—precision. A 95 % conviction level gives us Z values of one.96, per the normal tables, and so we get

((1.96)² (0.5) (0.5)) / (0.05)^two = 385.

So a random sample of 385 households in our target population should be plenty to give us the confidence levels we need.

Modification for the Cochran Formula for Sample Size Adding In Smaller Populations

If the population we're studying is small, we tin can change the sample size we calculated in the above formula by using this equation:

Here northward₀ is Cochran's sample size recommendation, North is the population size, and n is the new, adjusted sample size. In our earlier case, if at that place were just g households in the target population, nosotros would calculate

385 / (1 + ( 384 / 1000 )) = 278

So for this smaller population, all nosotros demand are 278 households in our sample; a substantially smaller sample size.

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Yamane's Formula

Yamane'southward formula is:
yamane's formula sample size

Where:

e = precision level
N = population size.

Watch the video for an example:

Yamane'southward Sample Size Formula

Can't see the video? Click here.

How to Find a Sample Size Given a Conviction Level and Width (unknown population standard difference)

Function two shows you lot how to find a sample size for a given conviction level and width (eastward.g. 95% CL, half-dozen% wide) for an unknown population standard departure .

Example question: 41% of Jacksonville residents said that they had been in a hurricane. How many adults should be surveyed to judge the truthful proportion of adults who have been in a hurricane, with a 95% conviction interval half dozen% wide?

Step i: Using the data given in the question, figure out the following variables:

Step 2: Multiply past . Gear up this number aside for a moment.
0.41 × 0.59 =0.2419

Step 3: Divide Z_a/ii by Eastward.
1.96 / .03 = 65.3333333

Step 4: Foursquare Step iii:
65.3333333 × 65.3333333 = 4268.44444

Footstep 5: Multiply Step 2 by Step 4:
0.2419 × 4268.44444 = 1,032.53671
= 1,033 people to survey.
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How to Find a Sample Size Given a Confidence Level and Width (known population standard deviation)

Part three shows y'all how to make up one's mind the appropriate sample size for a given confidence level and width, given that you know the population standard departure.

Case question: Suppose we want to know the average age of an Florida Country Higher pupil, plus or minus 0.5 years. We'd like to be 99% confident almost our result. From a previous study, we know that the standard divergence for the population is 2.ix.

Footstep ane: Notice z _a/twopast dividing the confidence level by two, and looking that area upwards in the z-table:
.99/2 = 0.495. The closest z-score for 0.495 is 2.58.

Pace 2: Multiply step 1 by the standard departure.
2.58 * two.9 = 7.482

Step three: Divide Step 2 by the margin of mistake. Our margin of error (from the question), is 0.v.
7.482/0.5 = 14.96

Step 4: Square Step 3.
14.96 * 14.96 = 223.8016

That'due south it! Like the caption? Check out our statistics how-to book, with a how-to for every elementary statistics problem type.
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Find a sample size to judge a population mean

Watch the video to find out how to find a sample size if you lot want to estimate means:

Sample Size for Population Hateful Conviction Level

Can't see the video? Click here.

How to find a sample size in Excel.

Lookout man the video or read the steps below:

How to select a sample using Data Assay in Excel 2013

How to utilize Excel Sampling to find a Sample

If you lot have a set of data and you know your sample size, yous tin can employ Excel's Information Analysis toolpak to select either a periodic sample or a random sample. A random sample is simply that — randomly selected from your data set. A periodic sample (besides chosen a systematic sample) is where Excel chooses the nth information item to include in your sample. For case, if y'all wanted to choose every 5th number from the post-obit list: 4, 5, vi, 7, viii, 9, 10, 11, 12, 13, 14, Excel would return 8 and thirteen (the fifth and 10th numbers in order).

If you don't know what sample size you need, calculate it before using the Data Assay tool (using the methods outlined at the height of this article). The Information Analysis tool tin help yous extract a sample, but it can't assist you lot make up one's mind on the size. Why? In that location are many "human" factors that go into selecting a sample size including budget, prior research (you lot can use a sample size from previous research) and tables synthetic from previous research.

How to use Excel Sampling to find a Sample: Steps

Step 1: Enter your information items into Excel. You can enter your data into rows or columns. Ensure the rows and columns are even; for example, enter data into column A to cell 12 and column B to cell 12.

Step 2: Click "Data" and then click "Information Analysis." If yous don't come across Data Analysis on your toolbar, load the Data Assay Toolpak.

Step 3: Click "Sampling" and then click "OK."

excel sampling.

Data entered into a worksheet for Excel sampling: the rows and columns are even.

Step iv: Click in the Input Range box and and then select your unabridged data ready.

Pace 5: Click either "Periodic Sampling" or "Random Sampling." If you cull periodic, enter the nth number (i.due east. every 5) and if you cull random sampling, enter the sample size.

Footstep half-dozen: Choose an output range. For example, click the "New Worksheet" button and Excel will return the sample in a new worksheet.

Pace 7: Click "OK."

That's it!

Check out our YouTube aqueduct for more Excel tips and help!
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Ways to Reduce Sample Size.
Effective Sample Size..
Diff sample size.

References

Bartlett, J. et al. (2001). Organizational Research: Determining Appropriate Sample Size in Survey Inquiry. Retrieved January 15, 2018 from: http://citeseerx.ist.psu.edu/viewdoc/download?doi=x.1.1.486.8295&rep=rep1&type=pdf.
Evans, One thousand.; Hastings, Northward.; and Peacock, B. Statistical Distributions, third ed. New York: Wiley, 2000.
Israel, G. (n.d.) Determining Sample Size. Academy of Florida IFAS Extension. Article posted on Tarleton State University website. Retrieved January thirteen, 2018 from https://www.tarleton.edu/academicassessment/documents/Samplesize.pdf.

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