03 Hypotheses

Question 1

errors in statistical hypothesis tests

Answer 1

Type 1: Rejecting the null hypothesis when it is true

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

Question 2

significance level

Answer 2

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

Question 3

significance probability

Answer 3

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.

Question 4

power

Answer 4

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

Question 5

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

Answer 5

power

Question 6

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.

Answer 6

significance probability

Question 7

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

Answer 7

significance level

Question 8

Rejecting the null hypothesis when it is true

Answer 8

Type 1 error

Question 9

Not rejecting the null hypothesis when it is false

Answer 9

Type 2 error

Question 10

standard error of the sample average

Answer 10

SE(\bar{Y}) = ^σ_ ̄Y = s_Y / root(n)

Question 11

sample variance

Answer 11

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

Question 12

an estimator for the population variance

Answer 12

sample variance

Question 13

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

Answer 13

sample variance

Question 14

SE( ̄Y) = ^σ_ ̄Y = s_Y / root(n)

Answer 14

standard error of the sample average

Question 15

The t-test is used when the ____ is unknown

Answer 15

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

Question 16

t-statistic

Answer 16

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

Question 17

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

Answer 17

t-statistic

Question 18

The t-statistic is t-distributed, which …

Answer 18

has heavier tails than the normal distribution.

Question 19

has heavier tails than the normal distribution

Answer 19

the t-distribution

Question 20

p-value

Answer 20

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.

Question 21

P-value when ̄Y is N( ̄Y0, σ^2_ ̄Y )

Answer 21

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

where ø is the standard normal cumulative distribution function

and Z = ( ̄Y - μ0) / σ_y

Question 22

P-value when distribution is unknown

Answer 22

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