03 Hypotheses Flashcards
errors in statistical hypothesis tests
Type 1: Rejecting the null hypothesis when it is true
Type 2: Not rejecting the null hypothesis when it is false
significance level
The significance level is the probability of rejecting the null hypothesis when it is in fact true
significance probability
The probability of drawing a statistic at least as adverse to the null hypothesis as the one you computed in your sample, assuming that the null hypothesis is true.
power
the probability of correctly rejecting the null hypothesis when the alternative is true
the probability of correctly rejecting the null hypothesis when the alternative is true
power
The probability of drawing a statistic at least as adverse to the null hypothesis as the one you computed in your sample, assuming that the null hypothesis is true.
significance probability
the probability of rejecting the null hypothesis when it is in fact true
significance level
Rejecting the null hypothesis when it is true
Type 1 error
Not rejecting the null hypothesis when it is false
Type 2 error
standard error of the sample average
SE(\bar{Y}) = ^σ_ ̄Y = s_Y / root(n)
sample variance
s^2_Y = 1 / (n - 1) * Sum[ (Yi - ̄Y)^2 ]
an estimator for the population variance
sample variance
s^2_Y = 1 / (n - 1) * Sum[ (Yi - ̄Y)^2 ]
sample variance
SE( ̄Y) = ^σ_ ̄Y = s_Y / root(n)
standard error of the sample average
The t-test is used when the ____ is unknown
The t-test is used when the population standard deviation is unknown
t-statistic
The t-statistic is the number of standard deviations your sample average is from the hypothesized mean.
the number of standard deviations your sample average is from the hypothesized mean.
t-statistic
The t-statistic is t-distributed, which …
has heavier tails than the normal distribution.
has heavier tails than the normal distribution
the t-distribution
p-value
The p-value is the probability of obtaining a test statistic (by random sampling variation) at least as adverse to the null hypothesis value as the statistic actually observed, assuming that the null hypothesis is correct.
P-value when ̄Y is N( ̄Y0, σ^2_ ̄Y )
p-value = P_H0( |Z| > |Zact| ) = 2ø(- |Zact|)
where ø is the standard normal cumulative distribution function
and Z = ( ̄Y - μ0) / σ_y
P-value when distribution is unknown
p−value = P_H0( |t| > |t^act| ) = 2ø(- |t^act|)
