A study that looked at beverage consumption used sample sizes that were much smaller than previous national surveys. One part of this study compared 20 children who were 7 to 10 years old with 5 who were 11 to 13. The younger children consumed an average of 8.4 oz of sweetened drinks per day while the older ones averaged 14.5 oz. The standard deviations were 10.7 oz and 8.4 oz respectively.
(a) Using the methods in this section, test the null hypothesis that the two groups of children consume equal amounts of sweetened drinks versus the two-sided alternative. Report all details of the significance-testing procedure with your conclusion. (Round your answers to three decimal places.)
(b) Give a 95% confidence interval for the difference in means. (Round your answers to four decimal places.)