1. Section 11.2: Carrying Out Significance Tests
AP Statistics
Section 11.2: Carrying Out Significance Tests

2. Objective: To be able to conduct a z-test.
z-test (test for 𝝁 when 𝝈 is provided):
Conditions:
Data is an SRS
Normality: a. Population is normal
OR b. n is sufficiently large so that the CLT
ensures that the sampling distribution of
𝑥 is normal.
Independence: a. Observations are independent
OR b. Population ≥ 10n

3. Hypotheses:
𝐻 0 :𝜇= 𝜇 𝐻 𝑎 :𝜇> 𝜇 Upper tail
𝜇< 𝜇 0 Lower tail
𝜇≠ 𝜇 sided
Rejection Region:
I will reject 𝐻 0 if my p-value < 𝛼. OR
I will reject 𝐻 0 if 𝑧> 𝑧 𝛼 ; 𝑧<− 𝑧 𝛼 ; 𝑧 > 𝑧 𝛼 2
Test Statistic & p-value
𝑧= 𝑥 − 𝜇 0 𝜎 𝑛 𝑃 𝑍>𝑧 ;𝑃 𝑍<𝑧 ;2∙𝑃(𝑍> 𝑧 )
5. State your conclusion in the context of the problem. (2 parts)

4. Tests from Confidence Intervals:
A level 𝛼 two-sided significance test rejects a hypothesis, 𝐻 0 :𝜇= 𝜇 0 , exactly when the value 𝜇 0 falls outside a level C confidence interval for μ.
Be careful when using a confidence interval to evaluate a significance test with a one-sided alternative. The 𝛼 level and the confidence level do not correspond directly as they do in a two-sided alternative.
Diagrams for 2-sided and 1-sided confidence intervals:

5. Example: Given 𝐻 0 :𝜇=64.5; 𝐻 𝑎 :𝜇≠64.5; 𝑥 =65.2; 𝜎=2.5 and n=100.
a. Calculate a 90% confidence interval for 𝜇.
Is there statistically significant evidence at the 0.10 level that the mean differs from the true value of 64.5? Explain without using a significance test.