HYPOTHESES TESTING TWO POPULATIONS

Estimating the difference between two pop’n means 

• Point estimator is the difference between the means of the pop’n 1 and 2 is sample mean1 - sample mean2 

INFERENCE st. deve known

Interval Estimation of M1-M2: both pop’n standard deviations known

1. Get the Za/2 score based on the confidence interval 

2. Get point estimate through the sample means

3. Get the interval estimate +/–

Interval estimate (where 1-a is the confidence coefficient)

INFERENCES ABOUT THE DIFFERENCE BETWEEN 2 POP’N MEANS WITH STANDARD DEVIATION UNKNOWN

• Use sample standard deviation (s)

• Replace za/2 with ta/2 

• Degrees of freedom is used to determine ta/2 

  • Get degrees of freedom (df)

  • Get a/2 of the significance level

  • Find the t a/2 in the t-table, wherein the df will be found on the left column area, and the a/2 will be found on the upper row area

• After getting the t a/2, substitute values on the interval estimation formula

HYPOTHESIS TESTING ABOUT POP’N MEAN INTERVAL ESTIMATE WITH BOTH STANDARD DEV’T KNOWN 

1. Develop the hypothesis using the two pop’n means against its hypothesized difference

2. Specify level of significance

3. Value of test-statistic (z-test since standard deviation is known)

4. Compute for the p-value in the z-table 

5. Determine whether to reject the null hypothesis

• P-value is less than or equal to significance level, reject null hypothesis