# 03 Hypotheses Flashcards

1
Q

errors in statistical hypothesis tests

A

Type 1: Rejecting the null hypothesis when it is true

Type 2: Not rejecting the null hypothesis when it is false

2
Q

significance level

A

The significance level is the probability of rejecting the null hypothesis when it is in fact true

3
Q

significance probability

A

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.

4
Q

power

A

the probability of correctly rejecting the null hypothesis when the alternative is true

5
Q

the probability of correctly rejecting the null hypothesis when the alternative is true

A

power

6
Q

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.

A

significance probability

7
Q

the probability of rejecting the null hypothesis when it is in fact true

A

significance level

8
Q

Rejecting the null hypothesis when it is true

A

Type 1 error

9
Q

Not rejecting the null hypothesis when it is false

A

Type 2 error

10
Q

standard error of the sample average

A

SE(\bar{Y}) = ^σ_ ̄Y = s_Y / root(n)

11
Q

sample variance

A

s^2_Y = 1 / (n - 1) * Sum[ (Yi - ̄Y)^2 ]

12
Q

an estimator for the population variance

A

sample variance

13
Q

s^2_Y = 1 / (n - 1) * Sum[ (Yi - ̄Y)^2 ]

A

sample variance

14
Q

SE( ̄Y) = ^σ_ ̄Y = s_Y / root(n)

A

standard error of the sample average

15
Q

The t-test is used when the ____ is unknown

A

The t-test is used when the population standard deviation is unknown

16
Q

t-statistic

A

The t-statistic is the number of standard deviations your sample average is from the hypothesized mean.

17
Q

the number of standard deviations your sample average is from the hypothesized mean.

A

t-statistic

18
Q

The t-statistic is t-distributed, which …

A

has heavier tails than the normal distribution.

19
Q

has heavier tails than the normal distribution

A

the t-distribution

20
Q

p-value

A

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.

21
Q

P-value when ̄Y is N( ̄Y0, σ^2_ ̄Y )

A

p-value = P_H0( |Z| > |Zact| ) = 2ø(- |Zact|)

where ø is the standard normal cumulative distribution function

and Z = ( ̄Y - μ0) / σ_y

22
Q

P-value when distribution is unknown

A

￼p−value = P_H0( |t| > |t^act| ) = 2ø(- |t^act|)