1 CH9. Hypothesis Testing (One Population) • Hypotheses are a pair of mutually exclusive, collectively exhaustive statements about the world. • One statement or the other must be true, but they cannot both be true. • H0: Null Hypothesis H1 (or Ha ): Alternative Hypothesis • Decision will be made to reject H0 or fail to reject (not reject) H0. • We can not accept H0, we can only fail to reject H0. • If H0 is rejected, we tentatively conclude H1 to be accepted. • Statements to be proved are located in H1. • A statistical hypothesis is a statement about the value of a population parameter ө (not statistic ). • A hypothesis test is a decision between two competing mutually exclusive and collectively exhaustive hypotheses about the value of parameter using a proper test statistic . • θ is a parameter and 0 θ is a specific value. • One/ two-side of the test is indicated by H1: Left-side test Right-side test Two-side test H0 : 0 θ θ ≥ 0 ( ) θ θ = H0 : 0 θ θ ≤ 0 ( ) θ θ = H0 : 0 θ θ = H1 : 0 θ θ < H1 : 0 θ θ > H1 : 0 θ θ ≠ • Ex 1) A tire company B claims that their newly developed tires’ average life expectancy (μ) is more than 7 yrs. Company B will build the hypotheses as follows: H0: vs. H1: • Ex 2) A consumer association claims that the average life expectancy of the newly developed tire from company B is significantly different from 7 yrs. The association will build the hypotheses as follows: H0: vs. H1: • Ex 3) A tire company D claims that the average life expectancy of the newly developed tire from company B is less than 7 yrs. Company D will build the hypotheses as follows: H0: vs. H1:
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CH9. Hypothesis Testing (One Population)ocw.sogang.ac.kr/rfile/2014/Business Statistics/CH9... · 2014-10-07 · 1 CH9. Hypothesis Testing (One Population) • Hypotheses are a pair
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CH9. Hypothesis Testing (One Population)
• Hypotheses are a pair of mutually exclusive, collectively exhaustive
statements about the world.
• One statement or the other must be true, but they cannot both be true.
• H0: Null Hypothesis
H1 (or Ha ): Alternative Hypothesis
• Decision will be made to reject H0 or fail to reject (not reject) H0.
• We can not accept H0, we can only fail to reject H0.
• If H0 is rejected, we tentatively conclude H1 to be accepted.
• Statements to be proved are located in H1.
• A statistical hypothesis is a statement about the value of a population
parameter ө (not statistic).
• A hypothesis test is a decision between two competing mutually exclusive
and collectively exhaustive hypotheses about the value of parameter using a