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Final Notes

# Final Notes - IS 310 Final Notes Chapter 9 Hypothesis Tests...

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IS 310 Final Notes Chapter 9: Hypothesis Tests 1. Developing Null and Alternative Hypotheses a. Hypothesis testing: used to determine whether a statement about the value of a population parameter should or should not be rejected. b. Null hypothesis: (denoted by H 0 ) tentative assumption about a population parameter. c. Alternative hypothesis: (denoted by H a ) is the opposite of H 0 . i. Alternative hypothesis is what the test is attempting to establish. ii. H a – What you are trying to prove! d. Hypothesis test about the value of a population mean µ must take one of the following three forms (where µ 0 is the hypothesized value of the population mean). i. One tailed (lower-tail) 1. H 0 : µ ≥ µ 0 2. H a : µ < µ 0 ii. One tailed (upper tail) 1. H 0 : µ ≤ µ 0 2. H a : µ > µ 0 iii. Two tailed 1. H 0 : µ = µ 0 2. H a : µ ≠ µ 0 3. P-value = 2(z-value) 2. Type I and Type II Errors

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3. Population Mean: σ Known a. Critical Value Approach to One Tailed Hypothesis Testing i. Use standard normal probability distribution table to find the z-value with an area of α in the lower (or upper) tail of the distribution. ii. iii. Confidence interval: + / za 2σn iv. Critical value: t he value of the test statistic that established the boundary of the rejection region. v. Rejection rule: 1. Lower tail: a. P-value approach: Reject H 0 if p-value ≤ α b. Critical value approach: Reject H 0 if z ≤ -z α 2. Upper tail: a. P-value approach: Reject H 0 if p-value ≤ α b. Critical value approach: Reject H 0 if z ≥ z α b. Steps of Hypothesis Testing i. Develop the null and alternative hypothesis ii. Specify the level of significance α iii. Collect the sample data and compute the test statistic (z).
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Final Notes - IS 310 Final Notes Chapter 9 Hypothesis Tests...

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