Comparisons Involving Means Learning Objectives 1. Be able to develop interval estimates and conduct hypothesis tests about the difference between two population means when EMBED Equation.DSMT4 and EMBED Equation.DSMT4 are known. 2. Know the properties of the sampling distribution of EMBED Equation . 3. Be able to use the t distribution to conduct statistical inferences about the difference between two population means when EMBED Equation.DSMT4 and EMBED Equation.DSMT4 are unknown. 4. Learn how to analyze the difference between two population means when the samples are independent and when the samples are matched. 5. Understand the principles of experimental design. 6. Be able to analyze a completely randomized design. 7. Understand how the analysis of variance procedure can be used to determine if the means of more than two populations are equal. 8. Know the assumptions necessary to use the analysis of variance procedure. 9. Understand the use of the F distribution in performing the analysis of variance procedure. 10. Know how to set up an ANOVA table and interpret the entries in the table. 11. Be able to use output from computer software packages to solve analysis of variance problems. Solutions 1. a. EMBED Equation 13.6 - 11.6 2 b. EMBED Equation.DSMT4 1.645 EMBED Equation EMBED Equation EMBED Equation.DSMT4 Mean loan amount for 2001 H0 EMBED Equation.DSMT4 Ha EMBED Equation.DSMT4 EMBED Equation p-value 1.0000 - .9850 .0150 p-value EMBED Equation.DSMT4 .05 reject H0. The mean loan amount has increased between 2001 and 2002. 7. a. EMBED Equation.DSMT4 Population mean 2002 EMBED Equation.DSMT4 Population mean 2003 H0 EMBED Equation.DSMT4 Ha EMBED Equation.DSMT4 b. With time in minutes, EMBED Equation.DSMT4 172 - 166 6 minutes c. EMBED Equation p-value 1.0000 - .9955 .0045 p-value EMBED Equation.DSMT4 .05 reject H0. The population mean duration of games in 2003 is less than
