In: Statistics and Probability
1. An experiment compared the ability of a group of chefs versus amateur cooks to taste spices in a dish. The researchers recorded the total number of spices each person identified and calculated the statistics below. Group n Mean Variance Chefs 10 8.3 1.3 Amateurs 10 5.5 3.1 (a) Calculate the 99% confidence interval for the difference between the means of the two groups. (b) Do you think the mean difference between the groups in the population could be 0.5? Why or why not? z-scores Confidence z Interval 80% 1.282 85% 1.440 90% 1.645 95% 1.960 99% 2.576 99.5% 2.807 99.9% 3.291 t-scores df 0.95 0.99 2 4.303 9.925 5 2.571 4.032 6 2.447 3.707 7 2.365 3.499 8 2.306 3.355 9 2.262 3.25 10 2.228 3.169 18 2.101 2.878 19 2.093 2.861 20 2.086 2.845 21 2.080 2.831