Estimating with Uncertainty Flashcards

1
Q

estimation

A

process of inferring a population parameter from sample data

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2
Q

how does the estimation of a parameter reflect the population parameter

A

almost NEVER the exact same as the value of the population parameter being estimated

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3
Q

what do we want to know about the estimate of a sample

A

how precise it is (how close to the true value in the population it is)

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4
Q

sampling distribution

A

probability distribution of all the values for an estimate that we MIGHT have obtained when sampled the population

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5
Q

what is the sampling distribution used to determine

A

how precise the estimate is

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6
Q

what does sampling distribution represent

A

the “population” of values for an estimate

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7
Q

how does the spread of sampling distribution depend on sample size

A

Larger the sample size = the narrower the sampling distribution = the more precise the estimate

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8
Q

standard error reflects

A

differences between an estimate and the target parameter = reflects the precision of an estimate

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9
Q

smaller vs larger standard error

A

smaller = more precise estimate

larger error = less precise estimate

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10
Q

what is the relationship between standard error and sample size

A

as sample size INCREASES the standard error DECREASES

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11
Q

Confidence intervals is used because it

A

Quantifies uncertainty about the value of a parameter

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12
Q

what are confidence intervals

A

Range of numbers surrounding the sample estimate that is likely to contain the unknown value of the population parameter

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13
Q

what is the 95% confidence interval for the mean

A

A range likely to contain the value of the true population mean which extends above and below the sample mean

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14
Q

what do the numbers between the upper and lower bounds for a confidence interval represent

A

most plausible values for the parameter

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15
Q

Values OUTSIDE the confidence interval are

A

less plausible for the true value of the parameter in the population

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16
Q

Width of the 95% confidence interval

A

measure of uncertainty about the true value of the parameter

17
Q

broad vs narrow confidence interval width

A

broad = uncertainty is high = data not informative about location of population parameter

narrow = uncertainty is low = data is informative about the location of population parameter

18
Q

how is the approximate of the 95% confidence interval for mean population calculated

A

adding (upper limit) or subtracting (lower limit) two standard errors from the sample mean

19
Q

Error bars

A

Lines on a graph extending outward from the sample estimate that illustrates precision of an estimate

20
Q

Y bar is the estimate of

A

mu (population mean)

21
Q

s is the estimate of

A

sigma (population standard deviation

22
Q

P hat is the estimate of

A

p the population proportion

23
Q

what must be known for estimates to be useful

A

the precision of said estimates

24
Q

what is the process of estimation

A

the process of inferring a population parameter from sample data

25
are estimates often the same as the population parameters
NO - chance events make samples different from the true pop parameter
26
sampling distribution of the estimate
probability distribution of ALL values for an estimate we MIGHT have obtained when sampling the population REPEATEDLY
27
sampling distribution of sample mean
sampling distribution = the probability distribution of values (for mean) that we MIGHT of obtained when sampling population repeatedly
28
what is key in regards to the sample mean distribution
the true value of the population (mu) is a CONSTANT - has one distinct value while the sample mean is a VARIABLE - changes with every sample distribution taken
29
when is the y bar sample unbiased
when it corresponds to mu (represents the exact value of the pop parameter)
30
how does sample size affect sampling distribution of mean
larger sample = narrower sample distribution = more precise the population estimate
31
standard error
for an estimate its the standard deviation of the estimate's sampling distribution
32
are large or small standard errors more precise
small errors = smaller standard deviation of data = values are tightly clustered around the true value
33
how to calculate Standard error of the sample mean (SEM)
SAMPLE standard deviation of variable Y divided by the sample size
34
confidence interval
range of values that surround a sample estimate that is LIKELY to contain the population parameter (but NOT ALWAYS)
35
95% confidence interval of the mean
range, extending above and beyond the sample mean, likely to contain the mean population parameter (mu)
36
can all numbers in the 95% C.L be plausible for the true value
YES - 95% CI does not give the EXACT value but a range that it COULD be in
37
are narrower or wider CI's more informative
narrower = more information for pop true value
38
error bars
lines that extend from sample estimates that give information about the precision of the estimate