hypothesis testing

is a sample in a bank likely to be representative of a population

no bc banks don’t randomly select their customers

what is an experimental unit

object upon which we collect data

what is a population

all items of interest

what is a variable

a characteristic of an individual experimental unit

what is a sample

a subset of the units of a population

2 requirements of random sampling

each member of the population has the same probability of being selected

each member of the population is chosen strictly by chance

what is the central tendency of a set of measurements

the tendency of the data to cluster or center about certain numerical values

symbol for sample mean

x with a line on top

symbol for population mean

mew

3 types of central tendency

mean

median

mode

what is the variability of a set of measurements

the spread of the data

3 ways of measuring variability

range

variance

standard deviation

symbol for variance and standard deviation for a sample

variance: s²

standard deviation: s

symbol for variance and standard deviation for a population

variance: sigma squared

standard deviation: sigma

what is an inference

an estimate about a population based on info contained in a sample

what is an unbiased estimate

mean of sampling distribution = population parameter

what is a biased estimate

mean of sampling distribution DOES NOT equal population parameter

use inference to find the expected value of the sample mean

it is the population mean

so the sample mean is an unbiased estimator of the population mean

(see picture)

what symbol would you give for the standard deviation of the distribution of a set of sample means

.

having a smaller sample is…

…less precise

why is a smaller sample less precise

standard deviation of the sampling distributions will be larger so there is more variance among the sample means

whats the difference between the standard deviation of the samplng distribution and a sample variance

sd of sampling distribution: variance of the samples themselves

sample variance: variance within a sample

whats the symbol for the mean of the sampling distributions?

.

what can the mean of the sampling distributions be equated to

population mean

whats the formula for the standard deviation of the sampling distribution

standard deviation over root n

explain the central limit theorem

[see picture!!!]

the larger the n, the more accurate the normal approximation

What is a confidence interval

An interval 1.96 standard deviations below and above the sample mean - which gives an area of 0.95 so its a 95% confidence interval

therefore, in a 95% confidence interval, the probability that a randomly selected interval will contain the population mean is…

…0.95

what is a statistical hypothesis

a statement about the numerical value of a population parameter

symbol for null hypothesis and alternative hypothesis

H nought and H alpha

how to start a hypothesis testing question

state the null hypothesis and the alternate one

what is a test statistic

a sample statistic that the researcher uses to decide between the null and alternative hypotheses

what is a type one error

rejecting null hypothesis when its actually true

how is a type one error denoted

alpha

what’s a type two error

accepting the null hypothesis when its actually false

how is a type two error denoted

beta

what else is alpha used to represent

the rejection region of a hypothesis test (works for both one and two tailed - see picture)

what is the p-value in a one tailed test

the probability of observing a test statistic as extreme as calculated, in the direction that the alternative hypothesis suggests

what is the p value in a two tailed test

2 x probability of observing a test statistic as extreme as calculated

when do we reject the null hypothesis

when the p value is less than your chosen value of alpha (significance level)

what would be the test statistic for a large sample test for the population mean

with z being the test statistic