6.2 P-values and tests of means

Question 1

What is the P-value (definition)
What is the P-value (in terms of significance level)

Answer 1

It is the probability of rejecting the null hypothesis, assuming the null is true
it is the smallest level of significance for which the null can be rejected

Question 2

What is the P-value, in terms of the tails of the test?

Answer 2

For a one tailed test, It is the probability that lies above the test statistic for upper tail test and below the test statistic for a lower tail

For a two tailed test, it is the probability that is above the positive value of the test statistic plus the probability that lies below the negative value of the test statistic

Question 3

What is the treatment of the P-value?

What is the treatment of a P-value for a two-tailed test?

Answer 3

Reject if the significance level is greater than the P-value

For a two tailed test… double the P-value

Question 4

How do you calculate the adjusted significance level?

Answer 4

Significance level x [rank of P-value/number of tests]

Question 5

What is the treatment of ranked P-values & adjusted significance levels?

Answer 5

True rejections are where the adjusted significance is greater to or less than the P-value

Question 6

When would you use a t-test?

How many degrees of freedom?

Answer 6

If normal distribution, and variance is unknown (regardless of sample size)

If non-normal, variance is unknown and large sample

n-1

Question 7

When would you use a Z-test?

Answer 7

If the variance is known

If non-normal, variance is known and large sample

Question 8

When could you not use a test?

Answer 8

If non-normal and small sample size, regardless of whether variance is known/unknown

Question 9

What are the critical values at 90%, 95% and 99% for a one and two tailed test?

Answer 9

One tailed

90 = 1.28 95 = 1.65 99 = 2.33

Two tailed

90 = 1.65 95 = 1.96 99 = 2.58