unknown but assumed equal \u03c3 1 and \u03c3 2 unknown not assumed equal

# Unknown but assumed equal σ 1 and σ 2 unknown not

• Rutgers University
• STATS 401
• Notes
• JaydipS
• 45
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unknown but assumed equal σ 1 and σ 2 unknown, not assumed equal
Chap 10-20 Population means, independent samples σ 1 and σ 2 known σ 1 and σ 2 unknown, large samples * σ 1 and σ 2 unknown but assumed equal σ 1 and σ 2 unknown, not assumed equal Where t has (n 1 + n 2 2) d.f., and 2 n n s 1 n s 1 n s 2 1 2 2 2 2 1 1 p 2 1 p 2 1 2 1 n 1 n 1 s μ μ x x t The test statistic for μ 1 μ 2 is:
Chap 10-21 Population means, independent samples σ 1 and σ 2 known σ 1 and σ 2 unknown, small samples The test statistic for μ 1 μ 2 is: * σ 1 and σ 2 unknown but assumed equal σ 1 and σ 2 unknown, not assumed equal 2 2 2 1 2 1 2 1 2 1 n s n s μ μ x x t Where t has d.f. given by 1 n /n s 1 n /n s ) /n s /n (s df 2 2 2 2 2 1 2 1 2 1 2 2 2 2 1 2 1
Chap 10-22 Two Population Means, Independent Samples Lower tail test: H 0 : μ 1 μ 2 0 H A : μ 1 μ 2 < 0 Upper tail test: H 0 : μ 1 μ 2 0 H A : μ 1 μ 2 > 0 Two-tailed test: H 0 : μ 1 μ 2 = 0 H A : μ 1 μ 2 0 /2 /2 -z -z /2 z z /2 Reject H 0 if z < -z Reject H 0 if z > z Reject H 0 if z < -z /2 or z > z /2 Hypothesis tests for μ 1 μ 2 Example: σ 1 and σ 2 known: