Term
| The Sampling Distribution of a Statistic |
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Definition
| The probability distribution that specifies the probabilities for all the possible values that the statistic can take. The idea of sampling distribution is to SEE THE PATTERN THAT EMERGES WHEN WE TAKE REPEATED SAMPLES, and compute a statistic from each one of them. |
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Term
| Sampling Distribution always refers to the ________ ________ of a statistic. |
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Definition
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| Every Statistic has a ________ ________. |
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Definition
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Term
| 2 types of statistics to study the sampling distribution: |
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Definition
sample proportion;
sample mean |
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Term
| Random values have a _________ this a pattern that emerges in repeated sampling. |
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Definition
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Term
| The statistics computed from different samples will vary, so they are _______ _______. |
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Term
| The computations we do in this chapter are still apart of the field of _________. |
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Definition
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Term
| In statistical inference, we are usually more interested in the proportion of people who answer yes to a certain question, for example, rather than the _____. |
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| We will use a sample proportion to estimate the true but unknown _______ _______ of successes in a binomial setting. |
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Definition
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Term
| Sample Proportion of successes: (formula) |
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Definition
| P(hat)=x/n= # of successes/ # of observations |
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Term
| X in P(hat)= x/n is the count of "_______" out of n _______ ________ trials, each having a ____________ p of success. |
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Definition
successes;
independent binomial;
probability |
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Term
| P(hat) and X are not the same. The proportion P(hat)must be between __ and ___. The count, X, is an integer between ___ and ___. |
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Definition
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Term
| Note that the sample proportion is actually an _______. |
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Definition
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Term
EXAMPLE: Suppose 30% of the population smokes (p=.30).
a) If you sample 100 people at random, what proportion in our sample will be smokers? |
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Definition
| Unknown, but probably pretty close to .3 |
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Term
| b) What would be the results if we took a different sample? |
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Definition
| Still unknown, but still close .3. |
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| c) what would be the results if each student in the class took their own sample and reported the results to the class? |
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Definition
| Bell shaped, centered around .3. |
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Term
| Sampling Distribution P(hat) |
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Definition
| we want to know the distribution of all the possible values of the sample proportion P(hat) can take in repeated sampling. |
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Term
| The count of successes has a binomial distribution under the right conditions: (2)_______ ,________. However, the sample proporiton P(hat) ______ (does/does not) have a binomial distribution since P(hat) can take any value between 0 and 1 - it is a _________ not a ______. |
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Definition
yes/no answer, n independent trials;
does not; count
Proportion |
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Term
Normal approximation:
Both expected number of successes and the expected number of failures are at least _____. So we _______ ___ (do not need to/ need to) check that _____ > (or equal to 15 and n(1-p)> (or equal to) _____. |
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Definition
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Term
| Mean of the distribution of P(hat): |
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Definition
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Term
| standard error of the distribution P(hat) |
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Definition
| P(hat) [Sqr root] p(1-p)/n |
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Term
| Note- we use the the term ______ ____ to refer to the _______ ______ of a sampling distribution, and distinguish it from the standard deviation of an ordinary probability distribution. |
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Definition
standard error;
standard deviation |
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Term
| Sampling Distribution of P(hat)is ______ ______, with mean= ___ and standard error=[formula of standard error] as long as the expected # of _________ (np) and ________ (n(1-p)) are each _____ or larger. |
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Definition
approximately normal;
p;
successes;
failures;
15 |
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