Hypothesis testing steps

Question: What is the mean age of our population?

  1. Data
    • Take a random sample
    • Sample mean = 27
    • Sample std = 3
    • n = 10
  2. Assumption
    • The population follows normal distribution
  3. Hypothesis
    • H0: Mean = 30
    • Ha: Mean != 30
  4. Pick test statistics
    • Z = (SampleMean – M0)/sigma_sample = (SampleMean – M0)/(sigma/sqrt(n))
    • Since we don’t know sigma, std of sample will be used instead of sigma –> No longer Z
  5. Distribution
    • t-distribution
  6. Decision rule
    • Minimize type 1 error (incorrect rejection of null hypothesis) = 5%
    • ==> table look up to find t distribution critical values (standard error) (e.g. 2.262 for 5% error)
  7. Calculate test statistic
    • t = (SampleMean – M0) /(sigma/sqrt(n))
    • t =(27-30)/(3/sqrt(10))= -3.15
  8. Statistical decision
    1. -3.15 < -2.262 ==> reject the null
    2. confidence interval
    3. Screen Shot 2015-12-30 at 4.04.43 AM
  9. Conclusion
  10. P-value

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

w

Connecting to %s