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Section 4

Section 4. Testing Two Variances. F Distribution. Use F Probability Distribution Two populations are independent Two populations each have a normal probability distribution S 1 2 > S 2 2 (Population 1 defined as population with larger sample variance). Properties of the F Distribution.

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Section 4

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  1. Section 4 Testing Two Variances

  2. F Distribution • Use F Probability Distribution • Two populations are independent • Two populations each have a normal probability distribution • S12 > S22 (Population 1 defined as population with larger sample variance)

  3. Properties of the F Distribution • Not symmetrical; skewed to the right • Values of F distribution are > 0 • dfN (Numerator) = n1 – 1 • dfD (Denominator) = n2 – 1

  4. Example • A large variance in blood chemistry components can result in health problems. A study was conducted concerning the glucose levels of pregnant and nonpregnant women. Medical researchers question if the variance of the glucose test results for nonpregnant women is different than for pregnant women. Use a 5% level of significance.

  5. Solution Nonpregnant: n1 = 10, s12 = 211.21 Pregnant: n2 = 8, s22 = 196.21 Ho: = H1: Test Statistic =

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