UF STA 2023 Exam 2

sampling distribution

a probability distribution that uses parameters to give probabilities of getting different values of statistics from the same population

if you're not given the standard deviation, how can you find it using the range?

St. D.=(range/6)

central limit theory

as sample size increases, sampling distributions begin to look more and more like the normal distribution, regardless of the shape of the population distribution

as sample size increases, the sampling distribution gets closer to the________

parameter

sampling distribution for means

normal approximation for quantitative variables

What two questions do you ask to determine if you can use normal approximation for means?

1. is the population normally distributed?

2. is the sample size at least n=30?

For a sampling distribution question, what are the 3 steps?

1. Does it meet the assumptions?

2. Distribution

3. score/probability

how to find probabilities from normal distribution using a z-table

1. convert both bounds to z-scores

2. draw area you're trying to find

3. look up the bounds on the z-table

sampling distributions for proportions

normal approximation for categorical variables

both p-hat and x-bar are known as________

unbiased estimators

What two questions do you ask to determine if you can use normal approximation for proportions?

1. is np>15

2. is n(1-p)>15

What is the difference between binomial distribution and the sampling distribution?

binomial is discrete and for x

sampling is continuous and for p-hat

p-hat=

x/n

confidence interval

an interval between two numbers, which are ___% confidence that the parameters in between

For confidence intervals and significance tests, we do NOT know ________

parameters

confidence level

a quantitative measure of how confident we are that the parameter is in the confidence interval

interval estimation

using intervals to estimate parameters

What are the two potential errors in interval estimation?

bias and variability

bias

systematic error, problem with point estimate (center)

bias is corrected through________

radomization

variability

random error, natural spread of the data could lower precision of interval estimate

variability is corrected through_______

increasing sample size

As sample size increases, confidence interval width______

decreases

As confidence level increases, confidence interval width______

increases

What happens to the width of the interval if we increase the confidence level and increase the sample size?

It entirely depends on the magnitude of effects. Could even cancel each other out, you just don't know

T-distribution

used with quantitative variables and small sample sizes

degrees of freedom

every t-distribution has a certain number of df's, df=n-1

Formula for t-scores

t= (estimator-mean)/standard error

T/F: For confidence intervals x-bar is always in the interval created

true, it is ALWAYS in the middle

The probability that the parameter is in any blank% interval is blank%. Once created, it is either_____or____.

0 or 1

standard error

s/sqrt(n)

Confidence intervals for means uses _-scores

t-scores

formula for confidence intervals for means

x-bar +/- (t-score)(standard error)

formula for determining sample size for mean

n=((z*s)/ME)^2

Confidence intervals for means proportions _-scores

z-scores

formula for confidence intervals for proportions

p-hat +/- (z-score)(sqrt( (p-hat(1-p-hat))/n))

What do you use for z-score to construct a 90% confidence interval for proportions?

1.645

What do you use for z-score to construct a 95% confidence interval for proportions?

1.960

If we wanted to lower the margin of error, but keep the same confidence level, what could we do?

increase the sample size

What do you do if you don't meet the assumptions for confidence intervals for proportions?

add two successes and two failures

ONLY DO IT ONCE

new p-hat=(x+2)/(n+4)

formula for determining sample size for proportions

n=((z*sqrt(p-hat(1-p-hat))/ME)^2

When we make inferences about ONE POPULATION PROPORTION, what assumptions do we need to make?

1. data is categorical

2. Data must be SRS

3. counts of successes and failures at least 15 each

Using the bootstrap method, how can you find the 90% confidence interval for the population standard deviation from these values?

use the 1st and 91st percentiles of these values

What do you use for z-score to construct a 90% confidence interval for proportions?

1.645

significance testing

have an idea of what parameter is, want to check if its right

null hypothesis

Ho: nothing is going on, the assumed value, "not guilty"

alternative hypothesis

Ha: what you think is going on, change in the norm, "guilty"

test statistic

a quantitative measure of how "weird" your sample is, z/t score

p-value

the probability of getting your test statistic given that the null hypothesis is true

significance level (alpha)

a cutoff value that determines which conclusion you will determine is correct

generally, if your p-value is less than (or equal to) your a-level, then you__________

reject the null hypothesis

if your p-value is more than your a-level then you____________

fail to reject the null hypothesis

test statistic formula

z=(p-hat-p)/(sqrt(p(1-p))/n)

standard error is the _________of the sample

standard deviation

bias and variability are independent of each other meaning a large sample will not_______

fix biased data