Analyzing Proportions Flashcards

1
Q

what is a proportion

A

the fraction of a population bearing some trait

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2
Q

how does proportion apply to statistic s

A

its the probability that an individual chosen from a population will bear the trait of interest

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3
Q

what numbers are proportions between

A

0 and 1

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4
Q

what does the binomial distribution apply towards

A

measurements that can be divided into two mutually exclusive groups

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5
Q

what is the general outcome for a binomial distribution/test

A

success (shows the desired outcome) or failure (does not show the desired outcome)

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6
Q

what is the binomial distribution

A

the probability distribution for the number of successes in a fixed number of trials when the probability of each success is THE SAME FOR EACH TRIAL

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7
Q

what variable represents number of successes

A

X

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8
Q

what variable represents the number of independent trials

A

n

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9
Q

what variable represents the probability of success for each trial

A

p-hat

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9
Q

what are important assumptions for n in a binomial distribution

A
  1. separate trials are independent
  2. probability of success (p) is the same in every trial
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10
Q

describe the binomial distribution equation

A
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11
Q

how to calculate “n chose X”

A
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12
Q

when do we have an unbiased estimate

A

when the mean sampling proportion= population proportion

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13
Q

how does a graph show a more precise sampling proportion value

A

the narrower spread of the data = more precise p-hat value

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14
Q

what is the binomial test

A

a test that uses data to test whether a population proportion (p) matches a null hypothesis expectation for the proportion

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15
Q

what is a null hypothesis for binomial test

A

relative frequency of successes in the population is the expected null hypothesis proportion (po)

16
Q

what is an alternative hypothesis for binomial test

A

the relative frequency of successes in the population is NOT the expected null hypothesis value

17
Q

is the alternative hypothesis in a binomial test two sided or one

A

two sided
( can either be above or below the null hypothesis expectation)

18
Q

when do we reject a null hypothesis in binomial testing

A

if the P-value calculated in below the significance level

19
Q

how do you calculate p-hat (the sample proportion)

20
Q

what is the binomial test OVERVIEW

A

whether a population proportion (p) matches a null expectation (po)

21
Q

what does a binomial test assume

A

random sample

22
Q

what is the test statistic in a binomial test

A

observed number of successes (X)

23
Q

when is an approximation of P values done

A

when n and X and huge numbers

24
does a binomial test give an exact or approximate P value
EXACT P value
25
what are the goals of estimating proportions
- estimate the population proportion (phat) - estimate the standard error of proportion (SE p-hat) - estimate confidence intervals for proportions
26
what is standard error
the standard deviation of the sampling distribution
27
how to calculate standard error of the proportion
28
how to calculate confidence intervals with Wald Method
where Z is 1.96
29
how to calculate confidence intervals with Agresti-Coull Method