Hypothesis Testing Part I & Part II

Hypothesis testing

· is used to solve 2 types of problems:

· To know if a population parameter (mean or variance) has changed (2 sided).

· To know if the population parameter is larger or smaller than before (1sided).

· Steps:

· Determine the null and alternative hypotheses

· Select a level of significance for the test ()

· Choose a test statistics (Z or t)

· Select a sample size

· Determine the decision rule

	H0 True	H0 False
Accept H0	Correct	Type II error
Reject H0	Type I error	Correct

· Reach a conclusion

· Types:

· Research - 1 sided (right sided)

· H0: μ = A

· Ha: μ > A

· Validity of claim - 1 sided (left sided)

· H0: μ = A

· Ha: μ < A

· Decision Type - 2 sided

· H0: μ = A

· Ha: μ ≠ A

· Examples (mean of 1 population):

· Known variance - "Z" test

· Unknown variance - "t" test

· A new engine designed by GSM is promised to increase fuel efficiency to 40mpg, a sample of 36 new engines designed by GSM shows an average of 38mpg, assume the standard deviation of population is known to be 6mpg, using α of 5%, conduct the test of hypothesis.

· The average salary of a bank manager in the US is $175,000, a sample of 16 banks selected at random in Chicago shows an average bank manager salary of $205,000 with standard deviation of $36,000. Using α of 5%, do the test of hypothesis to determine if the average bank manager salary in Chicago is different than the national average.

· Example (variance of 1 population):

· H0: σ2 = A

· Ha: σ2 ≠ A

· Using 𝜒2 test

·

· Example:

· According to a study conducted by GSM students the average age of all MBA students in the US is 28 years with standard deviation of 7 years. A sample of 11 MBA students taking Operations & Technology Management at GSM shows an average age of 25 years with standard deviation of 5 years. Using α of 5%, do the test of hypothesis to determine if the variance of this sample is significantly different from the Variance of all MBA students in the US.

· Test of hypothesis – means of 2 populations

· Case 1 – known variances

· Case 2 – Unknown variances:

· Assumption – equal variances – compute pooled variance

· Assumption – unequal variances – compute degrees of freedom

· 2-sided test – Case 1

· H0: μ1 μ2 = 0

· Ha: μ1 μ2 ≠ 0

· ( ) Z

· 2-sided test – Case 2

· H0: μ1 μ2 = 0

· Ha: μ1 μ2 ≠ 0

· ( ) t

· Paired observations – 1 population is tested before and after an experiment

· H0: = 0

· Ha: ≠ 0

·

· Test of hypothesis – Variances of 2 populations

· H0: =

· Ha: ≠

· F =

· Examples – Using MS Excel