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Biometry
Notation
27
Mathematics
Graduate
10/14/2012

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Term
X
Definition
Variable for a population
Term
xi
Definition
an individual observation for variable X
Term
muX
Definition
Population mean of variable X
Term
xbar
Definition
mean of the random sample of variable X
Term
muxbar
Definition
mean of sampling distribution of xbar
Term
sigmaX
Definition
Standard deviation of the true distribution of a population
Term
SX
Definition
Standard deviation of the variable X in a random sample
Term
Sigmaxbar
Definition
Standard deviation of the sampling distribution of the sample mean
Term
H0
Definition
Null hypothesis
Term
Ha
Definition
alternate hypothesis
Term
muo
Definition
mean for the null hypothesis
Term
p-value
Definition
When assuming that Ho is true, this is the probability that the test statistic would take a value as extreme or more extreme than that actually observed.
Term
alpha
Definition
The chosen significance level; it is also the probability of making a type I error
Term
beta
Definition
1-alpha; the probability of making a type II error
Term
Z
Definition
standardized variable of a standard normal distribution
Term
z
Definition
test statistic; estimate-hypothesized/standard deviation
Term
z*alpha
Definition
critical value of a Normal distribution at significance level alpha
Term
sX2
Definition
the sample variance of the variable X
Term
μsX2
Definition
mean of sampling distribution of sX2
Term
σX2
Definition
the variance of the distribution of variableX= Sum(xi-mux)2pi
Term
To determine the needed sample size n:
Definition

-need to know stdev x,

-need to choose alpha,

-need to know width of CI

Term
 If a margin of error is too large:
Definition

-Use a lower level of confidence (smaller C),

-increase the sample size (larger n),

-reduce sigma

Term
sample size for a desired margin of error, n=
Definition
((z*sigma)/m)^2
Term
The smaller the p-value...
Definition
the stronger the evidence against the null provided by the data
Term
To choose n, we need to:
Definition
1. know sigmax, 2. choose alpha, 3. desired power, 4. choose null hypothesis 
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