Appropriate Test Statistic Involving Population Mean

• Test Statistic

  • the numerical value calculated from sample data during hypothesis testing.
  • used to determine whether to reject the null hypothesis.
• Z-test (Population Variance is Known)

  • population is normally distributed
  • n (greater than or equal to) 30
  • population standard deviation is known
• T-test (Population Variance is Unknown)

  • population is normal or nearly normally distributed
  • n < 30
  • sample standard deviation is known; population standard deviation is unknown
• Z-test (Central Limit Theorem)

  • population may not be normally distributed
  • n > 30; considered extremely large
  • variance is known/unknown
• Critical Value

  • a point on the test distribution that is compared to the test statistic to determine whether to reject the null.
• Significance Level

  • the sensitivity of the test
  • a value of a (alpha) = 0.05 implies that the null hypothesis is rejected 5% of the time.
• Rejection Region

  • If the population variance is known, use the z-table for the standard normal distribution.
  • If the population variance is unknown, use the t-table for the distribution.