1. Aim: How do we test the difference between two means? HW#14: complete slide

2. Independent Samples Samples are independent samples when they are not related A t test is used to test the difference between means when the two samples are independent and when the samples are taken from two normally or approximately normally distributed populations

3. Use the t test when… Option 1 –Used when the variances of the populations are not equal Option 2 –Use when the variances are equal

4. Formula for the t test – for testing the difference between two means of a small independent sample Variances are assumed to be unequal

5. Formula for the t test – for testing the difference between two means of a small independent sample Variances are assumed to be equal: Where the degree of freedom are equal to

6. The average size of a farm in Indiana County, Pennsylvania, is 191 acres. Assume the data were obtained from two samples with standard deviations of 38 and 12 acres, respectively, and sample sizes of 8 and 10, respectively. Can it be concluded at α = 0.05 that the average size of the farms in the two countries is different? Assume the populations are normally distributed. Example

7. Procedure 1.Need to determine if the variances are equal if they did not give you any information about variances in the problem 1.State the hypothesis 2.Find the critical value (use f table) 3.Compute test value with f test 4.Make a decision 5.Summarize results 2.Decide which t test to use based on steps 1-5 1.State the hypothesis 2.Find the critical values 3.Compute test value with t test 4.Make a decision 5.Summarize results

9. Home Work 1. A researcher wishes to determine whether the salaries of professional nurses employed by private hospitals are higher than those of nurses employed by government-owned hospitals. She selects a sample of nurses from each type of hospital and conclude that the private hospitals pay more than the government hospitals? Assume that the population are approximately normally distributed. Use the P-value methods PrivateGovernment