# slide6 - Hypothesis Tests on the Mean H0 = 0 H1 0 Reject H...

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1 Hypothesis Tests on the Mean H 0 : µ = µ 0 H 1 : µ ≠ µ 0 n X Z 0 0 σ µ = 2 / 0 2 / 0 2 / 0 2 / 0 0 z Z z if H reject to Fail z Z or z Z if H Reject α α α α < > 2 Hypothesis Tests (one side) H 0 : µ = µ 0 H 1 : µ > µ 0 H 0 : µ = µ 0 H 1 : µ < µ 0 α z Z if H Reject 0 0 > α z Z if H Reject 0 0 <

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3 Example: two-sided test Suppose Guido takes a random sample of n =25 and obtains an average burn rate of 51.3 cm/s. Specs require that burn rate must be 50 cm/s, and the standard deviation is known to be 2 cm/s. He decides to specify a type I error probability (significance level) of 0.05. What conclusions can be drawn? 4 P-value The P-value is the smallest level of significance that would lead to rejection of the null hypothesis H0 with the given data. < = > = = = 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 : H : H : test for ) z ( : H : H : test for ) z ( 1 : H : H : test for |)] z (| 1 [ 2 P µ µ µ µ Φ µ µ µ µ Φ µ µ µ µ Φ
5 Probability of Type II Error The probability of the type II error is the probability that Z 0 falls between -z α /2 and z α /2 given that H 1 is true.

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