Chapter7.5_7.6 lecture notes

# Chapter7.5_7.6 lecture notes - Chapter 7.5 1 Tests of Ho...

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Chapter 7.5 . 1. Tests of Ho: μ = μ 0 (1) H 0 : μ = μ 0 σ known , and { X normal or n>29}. Test statistic : z= n X / 0 σ μ - . (2) H 0 : μ = μ 0 , σ unknown , n>29 . Test statistic : z= n S X / 0 μ - . Alternative Hypothesis Reject H 0 if P value μ < μ 0 z < -z α Pr(Z < z) μ > μ 0 z > z α Pr(Z > z) μ≠μ 0 |z| > z α /2 Pr(|Z| > |z|)=2Pr(Z>|z|) (3) H 0 : μ = μ 0 , σ unknown and X normal, (n<30) Test statistic : t= n S X / 0 μ - (t is observed value) Alternative Reject H 0 if P value μ < μ 0 t < - t α ,n-1 P(T n-1 < t) μ > μ 0 t > t α , n-1 P(T n-1 > t) μ≠μ 0 |t|>t α /2,n-1 2P(T n-1 >|t|) (4) H 0 : μ = μ 0 , If X not normal and n<30 -- consult a statistician. EXAMPLE: Suppose we are interested in knowing the mean number of days per week that students use a parking facility has changed. In the past years we had μ =2.8 days per week. We have reason to believe that the distribution of the number of days per week used per student has normal distribution. We sample n=9 students and observe that x =2.2 days and s=1.5. Test Ho: μ =2.8 days vs. H 1 : μ≠ 2.8 days at the α =0.05 level of significance. (a) First calculate the critical value for
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• Fall '03
• Mendell
• Statistics, Statistical hypothesis testing, \$89, \$95, \$98

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