Question

In each part, we have given the significance level and the P-value for a hypothesis test. For each case determine if the null hypothesis should be rejected. Write "reject" or "do not reject" (without quotations).

(a) α = 0.07, P = 0.06
(b) α = 0.06, P = 0.06
(c) α = 0.01, P = 0.06

Answer 1

a)
`\alpha=0.07 ,p_v =0.06`

Since
`p_v \leq \alpha` we "reject" the null hypothesis

b)
`\alpha=0.06 ,p_v =0.06`

Since
`p_v \leq \alpha` we "reject" the null hypothesis

c)
`\alpha=0.01 ,p_v =0.06`

Since
`p_v > \alpha` we " do not reject" the null hypothesis

Explanation:

Some previous concepts

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.

The null hypothesis attempts "to show that no variation exists between variables or that a single variable is no different than its mean"

The alternative hypothesis "is the hypothesis used in hypothesis testing that is contrary to the null hypothesis"

For any hypotehsis test we reject the null hypothesis is:

`p_v \leq \alpha`

In the other case we FAIL to reject the null hypothesis when:

`p_v >\alpha`

Solution to the problem

Part a

`\alpha=0.07 ,p_v =0.06`

Since
`p_v \leq \alpha` we "reject" the null hypothesis

Part b

`\alpha=0.06 ,p_v =0.06`

Since
`p_v \leq \alpha` we "reject" the null hypothesis

Part c

`\alpha=0.01 ,p_v =0.06`

Since
`p_v > \alpha` we " do not reject" the null hypothesis