BUSS1020 Chapter Notes - Chapter 9: Data Cleansing, Data Dredging, Null Hypothesis
28 May 2018
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CHAPTER 9: FUNDAMENTALS OF HYPOTHESIS TESTING – ONE-SAMPLE TESTS
FUNDAMENTALS OF HYPOTHESIS TESTING METHODOLOGY
• Hypothesis: a claim, often about a population parameter using a sample statistic
• The Null Hypothesis (H0):
o About population parameter
o Tests usually begin by assuming a null hypothesis is true
o May or may not be rejected in the test BUT cannot be proven outright
• The Alternative Hypothesis (H1):
o Represents conclusion reached by rejecting the null hypothesis = opposes null
o Generally is the hypothesis the researcher is trying to find evidence about
• The Test Statistic and Critical Values:
o Hypothesis testing uses sample data to determine how likely it is that H0 is true
o
X
“close” to pop mean à null not rejected
o
X
“far” from pop mean à null is rejected
• Errors:
o Type I error: rejecting a true null hypothesis à “false alarm”
§ α = P(reject null|null true)
o Type II error: failure to reject false null hypothesis à “missed opportunity”
§ β = P(not reject null|null false)
o Confidence coefficient (1 – α) = probability of not rejecting H0 when it is true
§ Confidence level = (1-α)*100%
o Power of statistical test (1 – ß) = probability of rejecting H0 when it is false
• Critical Value Approach: determine rejection regions based on level of confidence
o Decision rule: If test statistic falls in rejection region, reject H0
1. State null and alternative hypotheses, H0 and H1
2. Choose level of significance and sample size (alpha, n)
3. Determine appropriate test statistic and sampling distribution
4. Collect data, compute test statistic value
5. Determine critical values and compute test statistics
6. Make statistical decision and state managerial conclusion
• P-Value Approach: probability of getting a test statistic equal to or more extreme than sample result, if H0 is true
o Determine level of confidence you want, (1 – α)
o Compare α with p
o Decision Rule: |tSTAT| > tCRIT à
1. State null and alternative hypotheses
2. Choose level of significance and sample size (alpha, n)
3. Determine appropriate test statistic and sampling distribution
4. Compute test statistic and p-value
5. Make statistical decision and state conclusion
• Hypothesis Testing for the Mean (σ known)
o ZSTAT =
o ZCRIT = NORM.S.INV + P-value = NORM.S.DIST
• Hypothesis Testing for the Mean (σ unknown)
o When standard deviation, σ, is unknown use S in replacement and the t test for mean
o tSTAT = with (n – 1) degrees of freedom
o tCRIT = T.DIST + P-value = T.DIST
• Hypothesis Testing for the Proportion
o Use the Z distribution
Document Summary
Chapter 9: fundamentals of hypothesis testing one-sample tests. Fundamentals of hypothesis testing methodology: hypothesis: a claim, often about a population parameter using a sample statistic. The null hypothesis (h0): about population parameter, tests usually begin by assuming a null hypothesis is true, may or may not be rejected in the test but cannot be proven outright. The alternative hypothesis (h1): represents conclusion reached by rejecting the null hypothesis = opposes null, generally is the hypothesis the researcher is trying to find evidence about. Errors: type i error: rejecting a true null hypothesis false alarm . = p(reject null|null true: type ii error: failure to reject false null hypothesis missed opportunity . = p(not reject null|null false: confidence coefficient (1 ) = probability of not rejecting h0 when it is true. One-tail tests: alternative hypothesis focuses on a particular direction (e. g. < or >)
