Question: What is the mean age of our population?

- Data
- Take a random sample
- Sample mean = 27
- Sample std = 3
- n = 10

- Assumption
- The population follows normal distribution

- Hypothesis
- H0: Mean = 30
- Ha: Mean != 30

- 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

- Distribution
- 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)

- Calculate test statistic
- t = (SampleMean – M0) /(sigma/sqrt(n))
- t =(27-30)/(3/sqrt(10))= -3.15

- Statistical decision
- -3.15 < -2.262 ==> reject the null
- confidence interval

- Conclusion
- P-value

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