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AP Statistics β’ Section 12.1: Significance Tests in Practice β’ Objective: To be able to conduct a t-test and a paired t-test. t-test (test for π when π is unknown): 1. Conditions: SRS; Normality; Independence 2. Hypotheses: π»0 : π = π0 π»π : π > π0 ; π < π0 ; π β π0 3. Rejection Region: I will reject π»0 if my p-value < πΌ. OR I will reject π»0 if t > π‘πΌ,πβ1 ; t < βπ‘πΌ,πβ1 ; π‘ > π‘πΌ,πβ1 2 4. π‘= Test Statistic & p-value: π₯βπ0 π π π ππβ1 > π‘ ; π ππβ1 < π‘ ; 2 β π(ππβ1 > π‘ ) 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 ππ (Ex. ππ = ππ΄βπ΅ ) 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 βtypical student.β 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.