Download AP Statistics - Methacton School District

AP Statistics
• Section 12.1: Significance Tests in Practice
• Objective: To be able to conduct a t-test and a
paired t-test.
t-test (test for 𝝁 when 𝝈 is unknown):
1. Conditions: SRS; Normality; Independence
2. Hypotheses:
𝐻0 : 𝜇 = 𝜇0
𝐻𝑎 : 𝜇 > 𝜇0 ; 𝜇 < 𝜇0 ; 𝜇 ≠ 𝜇0
3. Rejection Region:
I will reject 𝐻0 if my p-value < 𝛼.
OR
I will reject 𝐻0 if t > 𝑡𝛼,𝑛−1 ; t < −𝑡𝛼,𝑛−1 ; 𝑡 > 𝑡𝛼,𝑛−1
2
4.
𝑡=
Test Statistic & p-value:
𝑥−𝜇0
𝑠
𝑛
𝑃 𝑇𝑛−1 > 𝑡 ; 𝑃 𝑇𝑛−1 < 𝑡 ; 2 ∙ 𝑃(𝑇𝑛−1 > 𝑡 )
5. State your conclusion in the context of the problem. (2 parts)
Paired t-test:
Used when data is collected in matched pairs setting.
1. Conditions: Same: *Check normality of the
DIFFERENCES.
2. Hypotheses: Same: *Define 𝜇𝑑 (Ex. 𝜇𝑑 = 𝜇𝐴−𝐵 )
3. Rejection Region: Same
4. Test Statistic & p-value: Same
5. State your conclusion in the context of the problem. (2
parts)
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
6.21. Conduct a significance test at the 0.01 level to
determine the answer to this question.