1.6 the role of P-values

Question 1

The p-value

Answer 1

defined as the area in the probability distribution outside the test statistic

The p
-value is a helpful measure because it is the smallest level of significance at which the null hypothesis can be rejected (test statistic exceeds critical value)

Question 2

how do we use the p value when we have to find a decision regarding the null hypothesis

Answer 2

p-value ≤ α: Reject the null hypothesis

p-value > α: Do not reject the null hypothesis

Question 3

Type I error occurs when??

Answer 3

if a true null hypothesis is mistakenly rejected

This probability is represented by α, which is the level of significance

Question 4

the false discovery rate (FDR).

Answer 4

The expected portion of the Type I error

Question 5

the false discovery approach

Answer 5

can be used by adjusting the p-values of the tests

used to lower the risk of rejecting a true null hypothesis (Type 1 error)

Question 6

the false discovery approach steps

Answer 6

1. Perform the hypothesis tests and list the p-values from all tests.
2. Rank the test results based on the p-values from lowest to highest.
3. Assuming that i is the sorted ranking of the test, the adjusted p-value is calculated by:

p∗(i) = α*(i/Number of tests)

4. Compare p∗(i) to the unadjusted p-value, p(i).
   –> The Rank i hypothesis test is statistically significant only if p(i) ≤ p∗(i)

Question 7

A t-test

Answer 7

commonly used to test the value of an underlying population mean

The t-distribution is similar to the standard normal distribution, but it is impacted by the degrees of freedom

–> Smaller degrees of freedom produce fatter tails

can be used for a population with unknown variance, provided the sample is large (≥ 30), or the population is approximately normally distributed

Question 8

t-test formula with a single mean and unknown variance

Answer 8

tn-1 = X¯− μ0 / sX¯

sX¯ = s/√n

The hypothesized mean is denoted by μ0

Question 9

The z-test

Answer 9

can also be used for a large sample even if the population variance is unknown

Question 10

z-test formula with a single mean and unknown variance

Answer 10

z = X¯− μ0 / sX¯

sX¯ = s/√n

The hypothesized mean is denoted by μ0

Question 11

z-test formula with known variance

Answer 11

z = X¯− μ0 / σX¯

where σX¯ = σ/√n

Question 12

The following rejection points are commonly used for a z-test:

Answer 12

z0.10 = 1.28

z0.05 = 1.645

z0.025 = 1.96

z0.01 = 2.33

z0.005 = 2.575