Statistics - Finding Critical Values

Statistics - Finding Critical Values

Definition of Critical Value

• A critical value is a point on the scale of the test statistic beyond which we reject the null hypothesis.
• It defines the boundaries for the confidence interval.

Key Concepts

• Critical values are associated with confidence levels and the sample size (n).
• They are found using a scoring distribution, often the z-distribution or t-distribution depending on if the population standard deviation is known or unknown.

Finding Critical Values

a) 90% Confidence Level with Sample Size n = 20

• To compute critical values (X):
  • For a 90% confidence level and n = 20:
  • Critical Values:
  • $X = 27.21$
  • $X = 10.11$

b) 99% Confidence Level with Sample Size n = 14

• For a 99% confidence level and n = 14:
  • Critical Values:
  • $X = 29.80$
  • $X = 4.10$

Summary of Calculated Critical Values

• For 90% Confidence (n=20):

  • $X_1 = 27.21$
  • $X_2 = 10.11$

• For 99% Confidence (n=14):

  • $X_1 = 29.80$
  • $X_2 = 4.10$