Hypothesis Testing for the Mean z-test!

Large Samples

Decision Rule Based on P-value

• If

• If 0reject then , HP

0reject tofail then , HP Examples:

1. The P-value for a hypothesis test is P = 0.023. What is your decision if the level of significance is

a. ?

b. ?01.005.0 Reject the null hypothesis

Fail to reject the null hypothesis

Finding the P-value for a Hypothesis TestAfter determining the hypothesis test’s

standardized test statistic and the test statistic’s corresponding area, do one of the following to find the P-value.

a. For a left-tailed test, P = (Area in left tail).

b. For a right-tailed test, P = (Area in right tail)

c. For a two-tailed test, P = 2(Area in tail of test statistic)

Example #1

1. Find the P-value for a left-tailed hypothesis test with a test statistic of z = -1.48. Decide whether to reject H0 if the level of significance is = 0.05.

Solution:

P(z = -1.48) = 0.069

Since p > 0.05, fail to reject the H0. Evidence at the 5% level supports the null hypothesis.

P = 0.069

Example #2

Find the P-value for a two-tailed hypothesis test with a test statistic of z = 2.31. Decide whether to reject H0 if the level of significance is = 0.01.

SolutionP(z > 2.31) = 0.0104

P= 2(Area in both tails) = .0219

Fail to reject the H0, there is enough evidence to support the H0 at the 1% level since p > 0.01.

P = 0.0104

P = 0.0104

Steps for z-Test

n

xz

Changing the level of significance to a z-score in order to find the critical

value. • Specify the level of significance• Decide whether the tail is left tailed, right

tailed, or two tailed.• Find the critical value(s) z0.

– Left tailed, find the z-score that corresponds to an area of

– Right tailed, find the z-score that corresponds to an area of 1 –

– Two tailed, find the z-scores that correspond to

and 1 -

2

1

2

1

NOW YOU GET TO DO PRACTICE 7.2!