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Hypothesis Testing
  • Null Hypothesis: H0
  • Alternative Hypothesis: Ha
  • Confidence Intervals (CI)
  • Hypothesis Tests for Variances:


o   Tests for a Single Population Variances

Chi-Square test

H0: σ2 = c 


 HA: σ2 ≠ c 


o   Tests for a two Population Variances:


F test

H0: σ12 – σ22 = 0
HA: σ12 – σ22 ≠ 0


  •  One Tailed Test:

Test if the value is greater than or less than K

H0; µ<=K vs. Ha: µ>K

  • Two Tailed Test:

Test if the value is different from K

H0; µ=0 vs. Ha: µ≠ 0

Sample Question



If standard deviation of a normal population is known to be 10 & the mean is hypothesized to be 8. Suppose a sample size of 100 is considered. What is the range of sample means in which hypothesis can be accepted at significance level of 0.05?


SE = 10/√100 =1


z = (x-µ)/ SE    = (x-8)/1

At 95% -1.96

Therefore 6.04







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