1. Aim: How do we test a comparison group? Exam Tomorrow

2. test hypotheses that compare means of two groups z test

3. Formula for the z Test for Comparing Two Means from Independent Populations If you are comparing means, your will always equal 0 unless told otherwise.

4. Procedure 1.State the hypotheses and identify the claim 2.Find the critical value(s) 3.Compute the test value 4.Make the decision 5.Summarize the results

5. Example A survey found that the average hotel room rate in New Orleans is $88.42 and the average room rate in Phoenix is $80.61. Assume the data were obtained from two samples of 50 hotels each and the standard deviations were $5.62 and $4.83, respectively. At α = 0.05, can it be concluded that there is significant difference in the rates?

6. Solution 1.State Hypothesis and identify claim 2.Find critical value 3.Calculate test value 4.Make a decision 5.Summarize the results Test value > critical value (reject null) There is enough evidence to support the claim that the means are not equal to each other

7. test the difference between two variances F test

8. Formula for the F Test The larger of the two variances is placed in the numerator regardless of the subscripts

9. Characteristics of the F Distribution 1.The values of F cannot be negative, because variances are always positive or zero 2.The distribution is positively skewed 3.The mean value of F is approximately equal to 1 4.The F distribution is a family of curves based on the degrees of freedom of the variance of the numerator and the degrees of freedom of the variance of the denominator

10. Steps 1.State the hypothesis and identify claim 2.Find the critical value 3.Compare the test values 4.Make the decision 5.Summarize the results

11. Example 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. Using α = 0.05, is there enough evidence to support the claim that the variances are equal?

12. Solution

13. test the difference between two means for small independent samples t test

15. 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 If information about the variance is not given to you, you must use the F test and test the variance to see if they are equal or unequal

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

17. 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

18. 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

19. 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