9.3 Distribution Needed for Hypothesis Testing

z-TEST: Hypothesis test of a single population mean [latex]\mu[/latex]:

• Sample data should be simple random sample
• Individual observations should be independent of other observations
• Population should be distributed normally or the sample size should be sufficiently large [latex](n \ge 30)[/latex] without any skew or outliers to ensure that the sampling distribution of the sample means [latex](\bar x)[/latex] is normal or approximately normal (Central Limit Theorem, UNIT 3)
• Population standard deviation σ is known (in reality σ is rarely known, though)

z-TEST: Hypothesis test of a single population proportion [latex]p[/latex]:

• Sample data should be simple random sample
• Ensure that the sampling distribution of [latex]\hat p[/latex] is approximately normal: [latex]np > 5[/latex] AND [latex]nq > 5[/latex]   where [latex]q = 1 - p[/latex].
  Some textbooks require [latex]np \ge 10[/latex] and [latex]nq \ge 10[/latex].
• Individual observations should be independent of other observations

t-TEST: Hypothesis test of a single population mean μ:

• Sample data should be simple random sample without any skew or outliers
• Population should be distributed normally or approximately normally distributed (Can relax this requirement for large samples)
• Population standard deviation σ is unknown
• Individual observations should be independent of other observations