Question

The test statistic of z=1.42 is obtained when testing the claim that p does not = 0.663. 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 alphaequals0.05​, should we reject Upper H 0 or should we fail to reject Upper H 0​?

Answer 1

Solution:

We are given that:

The test statistic is z = 1.42

Claim:

Part a) Identify the hypothesis test as being​ two-tailed, left-tailed, or​ right-tailed

Since claim is not equal to type, this is two tailed test.

Part b) Find the​ P-value

Since this is two tailed test, P-value is given by:

P-value = 2 X P( Z > z test statistic value)

P-value = 2 X ( 1 - P( Z < z test statistic value) )

P-value = 2 X ( 1 - P( Z < 1.42) )

Look in z table for z = 1.4 and 0.02 and find corresponding area.

P( Z < 1.42) = 0.9222

thus

P-value = 2 X ( 1 - P( Z < 1.42) )

P-value = 2 X ( 1 - 0.9222)

P-value = 2 X 0.0778

P-value = 0.1556

Part c) Using a significance level of ​, should we reject H0 or should we fail to reject H0.

Decision rule:

Reject H0, if P-value < 0.05 level of significance , otherwise we fail to reject H0.

Since P-value = 0.1556 > 0.05 level of significance , we fail to reject H0.