# Stats Ch 5 And 6

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variable is a variable that has a single numerical? value, determined by? chance, for each outcome of a procedure.
random variable
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random variable has infinitely many values associated with measurements.
continuous random variable
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The ....... of a discrete random variable represents the mean value of the outcomes.
expected value
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<0.05
unlikely/ unusual
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Which of the following is not a requirement of the binomial probability? distribution?
the trials must be dependent
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In the binomial probability? formula, the variable x represents the
probability of getting X successes among n trials
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?If, under a given? assumption, the probability of a particular observed event is extremely? small, we conclude that the assumption is probably not correct.
rare event rule
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The? _______ of a discrete random variable represents the mean value of the outcomes.
expected value
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To determine the probability that among the 17 offspring peas ,at least 16 have green pods, use the fact that....
P(at least 16)=p(16)+p(17)
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says that the range is about four times the standard deviation
range rule of thumb
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4*standard deviation
range rule of thumb
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Why must a continuity correction be used when using the normal approximation for the binomial? distribution?
The normal distribution is a continuous probability distribution being used as an approximation to the binomial distribution which is a discrete probability distribution.
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Sample means, variances and proportions
unbiased estimators
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Sample medians, ranges and standard deviations
biased estimators
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a variable (typically represented by x) that has a single numerical value, determined by chance, for each outcome of a procedure
random variable (X)
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a description that gives the probability for each value of the random variable, often expressed in the format of a graph, table, or formula
probability distribution
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a EXACT number of values or countable number of values
DISCRETE random variable
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infinitely many values, and those values can be associated with measurements
continuous random variable
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mean formula
mean=X*the probability of X
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standard deviation=
square root of ......(x-mean)^2 * the probability of (x)
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x successes among n trials is an unusually high number of successes if
p(X or more)<0.05
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x successes among n trials is an unusually low number of successes if
p(x or fewer)<0.05
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-The procedure has a fixed number of trials. -The trials must be independent. (The outcome of any individual trial doesn't affect the probabilities in the other trials.) -Each trial must have all outcomes classified into two categories (commonly referred to as success and failure). -The probability of a success remains the same in all trials.
binomial distribution
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p(s)=p
probability of success
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denotes a specific number of successes in n trials,
X
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denotes the fixed number of trials.
n
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denotes the probability of success in one of the n trials.
p
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denotes the probability of getting exactly x successes among the n trials.
p(x)
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When sampling without replacement, consider events to be independent if
n<0.05n
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range rule of thumb: maximum usual value minimum usual value
n+2(standard deviation) n-2(standard deviation)
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bell shaped- empirical rule when
np>5
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The Poisson distribution is sometimes used to approximate the binomial distribution when
n=large p=small
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Its graph is bell-shaped. Its mean is equal to 0 (? = 0). Its standard deviation is equal to 1 (? = 1).
STANDARD NORMAL distribution
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1. The total area under the curve must equal 1. 2. Every point on the curve must have a vertical height that is 0 or greater. (That is, the curve cannot fall below the x-axis.)
density curve
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use area to find....
probability
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normal distribution: how to find areas on calc
normal CDF
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z=
x-mean/s
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The points do not lie reasonably close to a straight line. The points show some systematic pattern that is not a straight-line pattern.
NOT a normal distribution
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Step 1. First sort the data by arranging the values in order from lowest to highest. Step 2. With a sample of size n, each value represents a proportion of 1/n of the sample. Using the known sample size n, identify the areas of 1/2n, 3/2n, and so on. These are the cumulative areas to the left of the corresponding sample values. Step 3. Use the standard normal distribution (Table A-2 or software or a calculator) to find the z scores corresponding to the cumulative left areas found in Step 2. (These are the z scores that are expected from a normally distributed sample.) Step 4. Match the original sorted data values with their corresponding z scores found in Step 3, then plot the points (x, y), where each x is an original sample value and y is the corresponding z score. Step 5. Examine the normal quantile plot and determine whether or not the distribution is normal.
Manual Construction of a Normal Quantile Plot
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is the distribution of all values of the statistic when all possible samples of the SAME SIZE N are taken from the SAME POPULATION
the sampling distribution of a statistic
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THE sampling distribution of the sample? mean
normal distribution NOT SKEWED TO LEFT OR RIGHT
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the distribution of sampling variance
SKEWED NOT NORMAL
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BIASED ESTIMATOR
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says that the computed values of the average will be distributed according to the normal distribution (commonly known as a "bell curve").