Question

The test statistic of zequals 2.03 is obtained when testing the claim that not equals 0.155. a. Identify the hypothesis test as being​ two-tailed, left-tailed, or​ right-tailed. b. Find the​ P-value. c. Using a significance level of alphaequals0.10​, should we reject Upper H 0 or should we fail to reject Upper H 0​

Answer 1

(a) It is a two-tailed test.

(b) The P-value is 0.042357.

(c) Since P-value < α, therefore we reject H₀.

Explanation:

Given information: The value of test statistic is z = 2.03.

(a)

We need to test the claim that p≠0.155.

Null hypothesis:
`H_0:p=0.155`

Alternative hypothesis:
`H_1:p\\eq 0.155`

It is a two-tailed test.

(b)

The level of significance is α=0.10.

The P-value for a two-tailed test, for a significance level of α=0.10 is 0.042357.

Therefore the P-value is 0.042357.

(c)

If P-value < α, then we reject H₀.

If P-value ≥ α, then we accept H₀.

where, α is level of significance.

It is given that α=0.10. Form part (b) it is clear that the P-value for a two-tailed test, for a significance level of α=0.10 is 0.042357.

0.042357 < 0.10

Since P-value < α, therefore we reject H₀.