Test of Hypothesis

# A random sample of 20 bofles results in a sample

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Unformatted text preview: = 0.83725, n = 15, S = 0.02456, α = 0.05, t 0.05,14 = 1.761 Procedure H 0 : µ = 0.82 1.Null Hypothesis 2. Alterna\$ve Hypotheses H1 : µ > 0.82 3. Test Sta\$s\$c X − µ 0 0.83725 − 0.82 t= = = 2.72 S/ n 0.02456 / 15 4. Cri\$cal Region Reject H 0 if t > tα ,n −1 → 2.72 > 1.761 5. Conclusion: Since .72 > 1.761 we reject H 0 : µ at the 0.05 = 0.82 2 , level of signiﬁcance that the mean coeﬃcient of res\$tu\$on exceeds 0.82. Dr. Hatem Elayat, AUC 23 Example (Contd.) Minitab Output Dr. Hatem Elayat, AUC 24 Test Concerning the Variance of a Normal Popula\$on Procedure 2 H0 : σ 2 = σ 0 1.Null Hypothesis 2. Alterna\$ve Hypotheses (can have three possible alterna\$ve hypotheses a) H1 : σ > σ 2 2 0 3. Test Sta\$s\$c 4. Cri\$cal Region 2 2 Reject if χ > χα ,n −1 b) H1 : σ < σ 2 ( n − 1) S 2 χ2 = 2 σ0 2 0 c ) H1 : σ ≠ σ 2 2 Reject if χ < χ1−α ,n −1 Dr. Hatem Elayat, AUC 2 2 0 2 χ 2 > χα / 2,n −1 Reject if 2 2 χ < χ25 α / 2,n −1 1− Example An automa\$c ﬁlling machine is used to ﬁll bofles with liquid detergent. A random sample of 20 bofles results in a sample variance of ﬁll volume of S 2 = 0.0153 (ﬂuid ounces)2. If the variance of ﬁll volume exceeds 0.01 (ﬂuid ounces)2, an unacceptable propor\$on of bofles will be under ﬁlled or overﬁlled. Is there evidence in the sample data to suggest that the manufacturer has a problem with under ﬁlled or overﬁlled bofles? Use α = 0.05 , and assume that ﬁll volume has a normal distribu\$on. Dr. Hatem Elayat, AUC 26 Example (Contd.) Data: n = 20, S = 0.01...
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