Sample Size Calculator
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`Sample Size Calculator
`
`Find Out The Sample Size
`This calculator computes the minimum numberof necessary samples to meet the desired
`statistical constraints.
`
`Confidence Level: ii
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`Margin of Error:
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`Population Proportion:
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`Use 50% if not sure
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`Population Size:
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`Leaveblankif unlimited population size.
`
`; (S
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`ll0)rs) 3 sr
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`Find Out the Margin of Error
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`This calculator gives out the margin of error or confidence interval of observation or
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`Result
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`Margin of error: 6.70%
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`This means,in this case, there is a 95% chancethat the real value is within +6.70% of the
`measured/surveyedvalue.
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`Confidence Level:
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`Sample Size:
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`200
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`Population Proportion:
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`Population Size:
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`3000
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`Leaveblankif unlimited population size.
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`is
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`Related
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`Standard Deviation CalculatorJProbability Calculator
`
`In statistics, information is often inferred about a population by studying a finite numberof
`individuals from that population, i.e. the population is sampled, andit is assumedthat
`characteristics of the sample are representative of the overall population. For the
`following,it is assumed that there is a population of individuals where some proportion, p,
`of the population is distinguishable from the other 1-p in some way; e.g., Pp may be the
`proportion of individuals who have brown hair, while the remaining 1-p haveblack, blond,
`red, etc. Thus, to estimate p in the population, a sample of n individuals could be taken
`from the population, and the sample proportion, p, calculated for sampled individuals who
`Exhibit 2166
`Exhibit 2166
`Page 01 of 04
`https://www calculator net/Sample-size-caiculator html?type=2&cl2=95&ss2=200&pc2=S0&ps2=3000&x=68&y=18#findei[1/25/2022 12:16:02 PM]
`
`U.S. Pat. 9,254, 338
`
`Mylan v. Regeneron
`IPR2021-00881
`
`Exhibit 2166
`Page 01 of 04
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`Sample Size Calculator
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`have brown hair. Unfortunately, unless the full population is sampled, the estimate p most
`likely won't equal the true value p, since p suffers from sampling noise,i.e. it depends on
`the particular individuals that were sampled. However, sampling statistics can be used to
`calculate what are called confidence intervals, which are an indication of how close the
`estimatepis to the true value p.
`
`Statistics of a Random Sample
`
`The uncertainty in a given random sample (namely that is expected that the proportion
`estimate, p, is a good, but not perfect, approximation for the true proportion p) can be
`summarized by saying that the estimate p is normally distributed with mean p and
`variance p(1-p)/n. For an explanation of why the sample estimate is normally distributed,
`study the Central Limit Theorem. As defined below, confidence level, confidenceintervals,
`and sample sizesare all calculated with respect to this sampling distribution. In short, the
`confidence interval gives an interval around p in which an estimate pis "likely" to be. The
`confidencelevel gives just how "likely" this is — e.g., a 95% confidence level indicates that
`it is expected that an estimateplies in the confidence interval for 95% of the random
`samples that could be taken. The confidence interval depends on the sample size, n (the
`variance of the sample distribution is inversely proportional to n, meaning that the
`estimate gets closer to the true proportion as n increases); thus, an acceptable error rate
`in the estimate can also beset, called the margin of error, €, and solved for the sample
`size required for the chosen confidence interval to be smaller than e; a calculation known
`as "sample size calculation."
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`Confidence Level
`
`The confidence level is a measureof certainty regarding how accurately a sample reflects
`the population being studied within a chosen confidence interval. The most commonly
`used confidence levels are 90%, 95%, and 99%, which eachhavetheir own
`corresponding z-scores (which can be found using an equation or widely available tables
`like the one provided below) based on the chosen confidence level. Note that using z-
`scores assumesthat the sampling distribution is normally distributed, as described above
`in "Statistics of a Random Sample." Given that an experiment or survey is repeated many
`times, the confidence level essentially indicates the percentageof the time that the
`resulting interval found from repeated tests will contain the true result.
`ConfidenceLevellz-score@)
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`ConfidenceInterval
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`In statistics, a confidenceinterval is an estimated rangeof likely values for a population
`parameter, for example, 40 + 2 or 40 + 5%. Taking the commonly used 95% confidence
`level as an example,if the same population were sampled multiple times, and interval
`estimates made on each occasion,in approximately 95% of the cases, the true population
`parameter would be contained within the interval. Note that the 95% probability refers to
`the reliability of the estimation procedure and notto a specific interval. Once aninterval is
`calculated,it either contains or does not contain the population parameterof interest.
`
`Exhibit 2166
`
`https:/Awww calculator net/Sample-size-caiculator html?type=2.&cl2=95&ss2=200&pc2=50&ps2=3000&x=68&y=1S#findci[1/25/2022 12:16:02 PM]
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`Page 02 of 04
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`Exhibit 2166
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`Sample Size Calculator
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`Somefactors that affect the width of a confidence interval include: size of the sample,
`confidence level, and variability within the sample.
`
`There are different equations that can be used to calculate confidenceintervals depending
`on factors such as whether the standard deviation is known or smaller samples (n<30) are
`involved, among others. The calculator provided on this page calculates the confidence
`interval for a proportion and usesthe following equations:
`a
`
`where
`Z is Z score
`P is the population proportion
`n and n' are sample size
`N is the population size
`
`Within statistics, a population is a set of events or elements that have some relevance
`regarding a given question or experiment. It can refer to an existing group of objects,
`systems, or even a hypothetical group of objects. Most commonly, however, population is
`used to refer to a group of people, whether they are the numberof employees in a
`company, numberof people within a certain age group of some geographic area,or
`numberof students in a university's library at any given time.
`
`It is important to note that the equation needs to be adjusted whenconsideringafinite
`population, as shown above. The (N-n)/(N-1) term in the finite population equation is
`referred to as the finite population correction factor, and is necessary because it cannot be
`assumed thatall individuals in a sample are independent. For example,if the study
`population involves 10 people in a room with ages ranging from 1 to 100, and one of those
`chosen hasan ageof 100, the next person chosenis morelikely to have a lower age. The
`finite population correction factor accounts for factors such as these. Refer below for an
`example of calculating a confidence interval with an unlimited population.
`
`EX: Given that 120 people work at Company Q,85 of which drink coffee daily, find the
`99% confidenceinterval of the true proportion of people whodrink coffee at Company Q
`on a daily basis.
`
`a
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`Sample Size Calculation
`
`Samplesize is a statistical concept that involves determining the numberof observations
`or replicates (the repetition of an experimental condition used to estimate the variability of
`a phenomenon)that should be includedin a statistical sample. It is an important aspect of
`any empirical study requiring that inferences be made about a population based ona
`sample. Essentially, sample sizes are used to represent parts of a population chosen for
`any given surveyor experiment. To carry out this calculation, set the margin oferror, €, or
`the maximum distance desired for the sample estimate to deviate from the true value. To
`do this, use the confidence interval equation above, but set the term to the right of the +
`sign equal to the margin of error, and solve for the resulting equation for sample size, n.
`The equation for calculating sample size is shown below.
`
`B
`
`where
`Z is the z score
`is the margin of error
`N is the population size
`P is the population proportion
`
`EX: Determine the sample size necessary to estimate the proportion of people shopping
`at a supermarketin the U.S.that identify as vegan with 95% confidence, and a margin of
`error of 5%. Assumea population proportion of 0.5, and unlimited population size.
`Rememberthat z for a 95% confidence level is 1.96. Refer to the table providedin the
`confidence level section for Z scores of a range of confidence levels.
`Bl
`
`Thus,for the case above, a sample size of at least 385 people would be necessary. In the
`above example, some studies estimate that approximately 6% of the U.S. population
`identify as vegan, so rather than assuming 0.5 for p, 0.06 would be used.If it was known
`Exhibit 2166
`
`https:/Awww calculator net/Sample-size-caiculator html?type=2.&cl2=95&ss2=200&pc2=50&ps2=3000&x=68&y=1S#findci[1/25/2022 12:16:02 PM]
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`Page 03 of 04
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`Exhibit 2166
`Page 03 of 04
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`Sample Size Calculator
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`that 40 out of 500 people that entered a particular supermarket on a given day were
`vegan, p̂ would then be 0.08.
`
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`https://www calculator net/sample-size-calculator html?type=2&cl2=95&ss2=200&pc2=50&ps2=3000&x=68&y=18#findci[1/25/2022 12:16:02 PM]
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`Exhibit 2166
`Page 04 of 04
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`