1. Section 12.1: Significance Tests in Practice
AP Statistics
Section 12.1: Significance Tests in Practice

2. Objective: To be able to conduct a t-test and a paired t-test.
t-test (test for 𝝁 when 𝝈 is unknown):
Conditions: SRS; Normality; Independence
Hypotheses:
𝐻 0 :𝜇= 𝜇 𝐻 𝑎 :𝜇> 𝜇 0 ; 𝜇< 𝜇 0 ; 𝜇≠ 𝜇 0
Rejection Region:
I will reject 𝐻 0 if my p-value < 𝛼. OR
I will reject 𝐻 0 if t> 𝑡 𝛼,𝑛−1 ; t<− 𝑡 𝛼,𝑛−1 ; 𝑡 > 𝑡 𝛼 2 ,𝑛−1
Test Statistic & p-value:
𝑡= 𝑥 − 𝜇 0 𝑠 𝑛 𝑃 𝑇 𝑛−1 >𝑡 ;𝑃 𝑇 𝑛−1 <𝑡 ;2∙𝑃( 𝑇 𝑛−1 > 𝑡 )
5. State your conclusion in the context of the problem. (2 parts)

3. Paired t-test:
Used when data is collected in matched pairs setting.
Conditions: Same: *Check normality of the DIFFERENCES.
Hypotheses: Same: *Define 𝜇 𝑑 (Ex. 𝜇 𝑑 = 𝜇 𝐴−𝐵 )
Rejection Region: Same
Test Statistic & p-value: Same
5. State your conclusion in the context of the problem. (2 parts)

4. Ex. 1 Attendance records at Methacton HS show that a typical student misses 6.4 days of school per year. A statistics student wants to conduct a study to see if seniors tend to be more absent then a “typical student.” The student randomly selects 30 seniors and finds that the mean of the sample is 9.3 with a standard deviation of Conduct a significance test at the 0.01 level to determine the answer to this question.