simple t test

a test statistic indicates that the sample data is

converted into a single specific statistic used to test the hypothesis

most test statistics

have the same basic structure and serve the same purpose as the z score

the difference between the sample mean (M) and the hypothesized population mean from the null hypothesis

(m - μ) larger difference indicates larger t value and more likely to reject null

the greater the difference between the sample mean and the population..

the bigger the z score

negative z scores will have the tail on the right

false

a sample underestimates the

variance

the sample with a n=8 will have __ degrees of freedom

7

high variability has patterns that are ___ to see

difficult

if the following 2 distribution are both converted to z score distributions their means will be the same

true

when standardizing a distribution the sample of the z score will be

the same

what does the CLT tell us about the distribution of sample means

if the shape is normal( BELL SHAPED), if the intiial population is normal or n > 30, THE MEAN OF THE DISTRIBUTION OF SAMPLE MEANS IS RQUAL TO THE MEAN OF THE ORIGINAL POPULATION

standard error allows us to estimate the difference between the sample mean and

the population mean

The CLT applies

the distribution of sample means for any population

the law of large numbers state that the larger the sample size

 the smaller the error between the sample mean and the population mean 

the standard deviation of a distrubiton of sample means is

the standard error

the shape of the distribution sample means with an n = 30 is

normal

critical region is determined by

the alpha level

type I errors are

the result of a very unlikely sample

as the s.d increases

the z gets smaller adn you are less likely to reject the null

as the number of tails increases

you are less likely to reject the null

a sample with the mean of 7 once transformed

the 7 will have a z score of 0

the numerator of a z score =

the deviation score

if you multiple the constant to each score in a distribution the standard deviation

increases by the constant

z score transformation..

relabels the values along the x axis

why is the variability of a sample less than the variability of the population

the sample has less extreme scores

variability of the scores

is measured by the standard deviation or the variance or in this case the standard error

as variability gets larger

the smaller the z score

the number of scores in the sample:

the larger the z score

what test can reject with smaller difference between sample mean and population mean

one tailed test can reject with smaller difference between sample and population

level of significance: a=.05, one tailed

±1.64

level of significance: a=.05, two tailed

±1.96

level of significance: a=.01, one tailed

±2.33

level of significance: a=.01, two tailed

±2.58

what is the problem with z score

it assumes population standard deviation is known need σ to compute standard error

the denominator of hte z score is

standard erro

σ tells us

how much scores vary in the entire population

standard error tells us

how much sample means vary from sample to sample

if the value of the real standard error is unknown 𝝈M

an estimated standard error (Sm) is used to estimate the real standard error

estimated standard error is computed with the

sample variance S² or sample standard deviation , S

estimated standard error provides

provides an estimate of the standard distance between a sample mena, M and the population mean µ

estimated standard error formula

t test

when calculating sample variance using n-1 you get

a better t stat closer resembles a z score

t distribution is normal

tends to be a little flatter and spread out than the z distribution

t distrubtion is the complete set of t values for

every possible random sample for a specific (n)

to compute a t statistic you only need

a null hypothesis and a sample from the unknown population

simple t test for

one sample and dont know the population standard deviation

what factors influence the outcome of a t test

size of n and magnitude of vairance

larger n…

increases the likelihood of rejecting the null

larger variance

reduces the likelihood of rejecting the null

larger variance

smaller t test

research design that uses a separate group of subjects for each treatment condition

independent measure research design

independent treatment design hypotheses

tests for data from 2 separate samples

independent treatment design evaluates the

mean difference between 2 treatment conditions

goal of independent measures research study

evaluate the mean difference between 2 populations or between 2 treatment conditions

difference between means is

2 sampl means (M1-M2) to evaluate the hypothesis about

2 population means  (µ1 - µ2) 

in an independent measures study the t =

S(M1-M2) measures

the expected error when a sample mean difference represents a population mean difference

with independent measures t, the difference betwee nsample means is divided by the

estimated standard error associated with the sample mean difference

standard error of M1-M2

a measure of tje standard or average distance between a sample statistic and population parameter

estimated standard error of M1 - M2 tells us

how much difference to reasonable expect between 2 sample means if the null is true (Ho: µ1 = µ2)