Mod 5 Flashcards by Shanelle Cabuhat

What is sampling variability?

the observed value of a statistic varies from sample to sample depending on the particular sample selected

statistic is a random variable as the value varies from sample to sample

How well did you know this?

Not at all

Perfectly

What is sampling distribution?

the distribution or collection of all possible values for a statistic for repeated samples of the same size

how the statistics vary under repeated sampling
the statistic has a distribution because values differ from sample to sample (if you take a different sample, you’ll get a diff value for that statistic)

How well did you know this?

Not at all

Perfectly

Does a statistic vary?

Because the sample statistic is a variable, it varies from sample to sample (if you take different sample, you’ll compute a different statistic or p^)

How well did you know this?

Not at all

Perfectly

What a sampling distribution describe?

the sample-to-sample variability of a statistic
it shows all possible sample statistics that we could obtain from samples of the same size of a population

How well did you know this?

Not at all

Perfectly

What is the standard deviation of the sampling distribution of a statistic?

measures how values of the sample statistic might vary across different samples from same population

How well did you know this?

Not at all

Perfectly

How does standard deviation of sampling distribution related to sample size (n)?

As n INCREASES, the standard deviation of the sampling distribution DECREASES
When n INCREASES, the statistic estimates the parameter more accurately

How well did you know this?

Not at all

Perfectly

Notation for sample proportion

sample proportion (p^)

How well did you know this?

Not at all

Perfectly

Notation for population proportion

true population proportion (p)

How well did you know this?

Not at all

Perfectly

What is the sampling distribution for a single proportion?

P^ = x/n
if it was a census, you’d have true population proportion (p)

How well did you know this?

Not at all

Perfectly

What happens to the standard deviation of a sampling distribution if sample size (n) increases?

as n INCREASES, standard deviation of a sampling distribution decreases

How well did you know this?

Not at all

Perfectly

What is the center of the sampling distribution?

mean/center of sampling distribution is the true population parameter (p)

p^ ~ AN (p, square root of p(1-p)/n)

How well did you know this?

Not at all

Perfectly

What is the spread of the sampling distribution?

standard deviation
standard error

p^ ~ AN (p, square root of p(1-p)/n)

How well did you know this?

Not at all

Perfectly

What is standard error of sampling distribution?

estimating the standard deviation of a sample distribution using sample data

replaces p with p^ in the standard deviation expression

SE (p^) = square root of p^(1-p^)/n

How well did you know this?

Not at all

Perfectly

What happens to standard deviation/error if sample size (n) increases?

Because of the square root,

Increase sample size (n) four times, cuts the standard deviation in half
Increase sample size nine times, then the spread goes down to a third

How well did you know this?

Not at all

Perfectly

When is the shape of the sampling distribution approximately normal?

np and n(1-p) ≥ 10

How well did you know this?

Not at all

Perfectly

What is the shape of the distribution of p^?

p^ cannot be binomial or uniform; only approximately normal

conditions:
- sample taken from population 10x larger than sample
- np and n(1-p) ≥ 10

How well did you know this?

Not at all

Perfectly

How do you use the sampling distribution of p^ to compute probabilities involving p^?

estimate population proportion (p) with sample proportion (p^)
p^ ~ AN (p, p(1-p)/n)
Conditions: good data collection, random sample taken from population is at least 10 times larger than the sample, np AND n(1-p) ≥ 10
normcdf to compute probabilities

What are the parameters of a binomial random variable?

X ~ binom(n,p)

What are intervals?

p^ +/- z* or number of standard deviations away (standard erorr)

z* = 95% or 2 standard deviations away from the mean

What is a point estimate?

A single number that is our best guess for the parameter
- doesn’t tell us how close the estimate is likely to be to the parameter

What is an interval estimate?

An interval of numbers within which the parameter value is believed to fall

includes a range of plausible values which can capture the true parameter (p) of the point estimate
includes margin of error

What are the differences between statistic vs population characteristics

statistic
- estimate
- changes based on the sample we drew
- follows a distribution

population characteristic
- fixed value
- doesn’t change
- unknown when conducting inference

What are the properties of a good estimator?

unbiased: sampling distribution of the estimator is centered at population characteristic (p) – the center of the statistic is the thing you’re trying to estimate
precise/accuracy: an accurate estimator falls closer to the parameter than others; has relatively small standard deviation

What is margin of error?

the maximum likely estimation error (unusual for an estimate to differ from the actual value of the population characteristic by more than the margin of error)

How far off we expect p^ to be from true p thus use standard deviation of sampling distribution

What is the formula of margin of error?

z* x square root of p^(1-p^)/n

Sample size on margin of error: What happens if sample size (n) increases? What happens if confidence level (90% to 95%) increases?

- as n INCREASES, margin of error decreases - as confidence level INCREASES, margin of error for a confidence interval increases

What is the formula of confidence interval for a single proportion?

point estimate (p^) +/- z* (standard error of p^)

What is confidence level?

confidence in the method to produce an interval that contains the parameter – a number chosen to be close to 1, most commonly 0.95 - The success rate of the method used to construct the interval to include the true population proportion (p) - “We are 95% confident that the method produces an interval that contains the true parameter” - Not a probability statement

What is a common mis-statement for confidence level?

phrasing confidence level as the probability the parameter is in the interval - p is fixed - interval is random

What is the confidence interval?

gives a range of plausible values for the true population parameter

Under which conditions can you use the large sample confidence interval for a population proportion?

np^ and n(1-p^) ≥ 10 Another condition: at least 10 successes and 10 failures

What happens to the width/margin of error of a confidence interval if the sample size (n) is increased?

as n INCREASES, width of a confidence interval decreases

What is the EMCCC method?

Estimate: estimate true proportion, p using p^ Method: large-sample confidence interval for single proportion Check conditions: np^ and n(1-p^) ≥ 10 Calculate: confidence interval (point estimate +/- margin error) Communicate: results whether it is a plausible interval or interpretation of confidence level

How do you get the critical value z* for any confidence level?

invnorm (left tail area, 0, 1) left tail area = the confidence level + left over Ex: “Find z* for 80% confidence level” invnorm (0.90, 0, 1) = 1.282

What is confidence interval? What is it not?

gives a range of plausible values for the population characteristic - NOT a probability that the characteristic is in the interval - The characteristic is fixed. - The sample we chose and interval we computed is what was random

What is the interpretation of a confidence level?

expresses our confidence in the method. The method will produce an interval that captures the true characteristic 95% of the time and misses it 5% of the time - Do NOT make probability statements about true population proportion, p (only that our sample gave an interval that covered the true p) - if we used 95% confidence interval method to estimate population proportions, then about 95% of those intervals would contain the population proportion - With probability of 0.05, the method produces a confidence interval that misses the truth 0.05 of the time

How do you determine how many intervals you would miss if you used the method?

Multiply n by the complement of confidence level to determine how many you missed EX: 95% confidence level n x 0.05 = how many intervals you'd miss using this method

What happens to width/margin of error if confidence level increases?

as confidence level INCREASES, width of interval also increases - To be more confident that we included the true p, you have to have a wider value

What happens to width/margin of error if sample size increases?

as n INCREASES, the width of the interval decreases (the margin of error decreases)

How do you compute sample size needed to achieve a desired margin of error for a population proportion (p) at a desired level of confidence

n = (z*)^2 x p(1-p) /m^2 If p is not known, use p = 0.5

Mod 5 Flashcards

Chapter 8 & 9