Studied by 2 peoplesignificance test
Ā a formal procedure for using observed data to decide between two competing claims (called hypotheses) about given parameters
null hypothesis (Ho)
the claim that we weigh evidence against in a significance test
alternative hypothesis (Ha)
the claim that we are trying to find evidence for
one-sided alternative hypothesis
states that a parameter is greater than the null value or if it states that the parameter is less than the null value
two-sided alternative hypothesis
Ā states that the parameter is different from the null value (it could be either greater than or less than)
always state null and alternative hypotheses in terms of ______________
population parameters (NOT sample statistics)
if the p-value is less than or equal to the significance level (alpha)
reject HoĀ and conclude there is convincing evidence for Ha (in context)
if the p-value is greater than the significance level (alpha)
fail to reject HoĀ and conclude there is not convincing evidence for Ha (in context)
significance level Ī±
Ā the value that we use as a boundary for deciding whether an observed result is unlikely to happen by chance alone when the null hypothesis is true
Type I error
Ā if we reject Ho Ā when HoĀ is true ā> the data give convincing evidence that Ha is true when it really isnāt
Type II error
occurs if we fail to reject Ho when Ha is true ā> the data do not give us convincing evidence that Ha is true when it really is
probability of a type __ error is equal to the significance level
I
Ho true, reject Ho = _____ error
type I
Ha true, fail to reject Ho = _____ error
type II
Ho true/fail to reject Ho OR Ha true/reject Ho
correct conclusion
relationship between type I and type II errors
s the probability of a Type I error increases, the probability of a Type II error decreases
type I error is also known as a false ______
positive
type II error is also known as a false ______
negative
condition for significance test about a proportion - RANDOM
Ā the data come from a random sample from the population of interest
condition for significance test about a proportion - INDEPENDENT
10% condition: n < 0.10N
condition for significance test about a proportion - NORMAL
large counts condition ā both np0 and n(1-p0) are at least 10.
p0
Ā our hypothesized population proportion (aka the proportion we are assuming is true in our null hypothesis)
standardized test statistic
measures how far a sample statistic is from what we would expect if the null hypothesis were true, in standard deviation units
equation for standardized test statistic
(statistic-parameter)/standard deviation (error) of statistic
standardized test statistic if we KNOW the population standard deviation is ___
z
standardized test statistic if we DO NOT KNOW the population standard deviation is _____
t
power
the probability that the test will find convincing evidence for Ha when a specific alternative value of the parameter is true OR probability that we find convincing evidence that the alternative hypothesis is true, given that the alternative hypothesis really is true
equation for power
Power = 1 - P(Type II Error)
equation for probability of type II error
P(Type II Error) = 1 - Power
to increase power:
______ sample size (n)
______ significance level (Ī±)
_______ distance between null and alternative parameter values
INCREASE
condition for performing a significance test about a difference between two proportions (RANDOM)
the data come from two independent random samples or from two groups in a randomized experiment
condition for performing a significance test about a difference between two proportions (INDEPENDENT)
10% condition: n1 < 0.10N AND n2 < 0.10N
condition for performing a significance test about a difference between two proportions (NORMAL)
Ā Large Counts Condition: expected numbers of successes and failures in each sample or group are all at least 10Ā (use p-hat cbmbined)
equation for p-hat combined
the Normal condition for a significance test about a mean can be satisfied in these 3 ways:
Ā 1) told the population is Normal
2) n is large (greater than 30, per the CLT)
3) graph and sketch a dotplot/histogram and assess shape (look for massive skew or outliers)
formula for one-sample t-test for means
in what situation should you select āpooledā on your calculator?
NEVER
equation for degrees of freedom
df = n-1
inference procedure for paired data
one-sample t procedures for mean difference
inference procedure for quantitative data from independent random samples of two populations of interest/groups in a randomized experiment
twp-sample t-tet for mu1-mu2
if a condition is NOT metā¦
"although this condition has not been satisfied,
we will assume that it has been, and proceed
with caution."
characteristics of a paired t test
-one sample (data are paired)
-mean of differencces
-subtract, then average
characteristics of a two-sample t test
-two independent samples/groups
-difference of means mu1-mu2
-average, then subtract
Note
Flashcard