Question

F-test theory question. I just need help with # 32.

Applications the Ftest in Excel, test the set of data you created for Apri in Q17. Show that variances are significantly different April's and Betty's 1. Verity that the Welch-Satterthwaite formula yields the value 6.440 for Evan and Fred's data. To simplify the calculation, use the variances given in the Excel output. pose you measured dissolved CO, in Brand X soda and BrandY soda, and found that Brand X a standard deviation twice that of Brand Y.What is Fx? Find a more complete Fen ta D.C. Harris, Quantitative Chemical Analysis 8th Ed. page 81, 's soda had mplete F table such as the one in Assume that you make the same number of easurements on both brands. U in order to conclude that the difference in standard deviations is significant se the table to determine how many many measurements would you need 33-Add the value 12.9 to Evan's data and repeat the Ftest. Repeat both ttests as well. What happens to the t values? Do the ttests give the same result? 34, Remove one of the 12.2 values from Fred's data and repeat the Ftest. Repeat both t tests as well. What happens to the tcae values? Do the t tests give the same result? 35. Show that the two formulas for tcc are equal when either a) n,-n, or b) s,-, 36. Show that the Welch-Satterthwaite formula simplifies to 2n-2 when s,-s, and n,-n, 37, Two students new to analytical chemistry each perform five identical acid-base titrations. They report standard deviations of 0.25 ml and 0.42 ml for the five titrations. Are their standard deviations significantly different? e serum calcium concentrations of seven patients with hypoparathyroidism are compared with those of seven healthy patients. The seven patients with the disease showed calcium levels of 8.12, 7.98, 8.06, 8.20, 8.08, 8.15, and 8.22 mg/dL, while the seven healthy patients showed calcium levels of 8.82, 8.91, 9.23, 10.02 9.67, 9.34, and 9.41 mg/dL. Is there a significant difference in the variance of serum calcium concentration for these two groups? Which t test must be used? Is there a significant difference in the average serum calcium concentration for these two groups? 9, Two new methods of measuring calcium in serum are compared. For five replicate measurements and 9.21 mg/dL. Do the two methods have significantly different means and standard deviations? must be used? 9.21, and 9.27 mg/dL, while the second method gave 9.20, 9.22, 9.23, 9.22 method gave 9.23, 9.26, 9.23,

Answer 1

$32.~F_{calc}=\frac{s_x^2}{s_y^2}=2^2=4~where,~s_x=standard~deviation~of~X's~soda\\ and~s_y=standard~deviation~of~Y's~soda~and~s_x=2s_y.\\ We~reject~H_0:\sigma_x^2=\sigma_y^2~if~F_{calc}>F_{0.05,n_1-1,n_2-1}~or~F<F_{0.95,n_1-1,n_2-1}\\ Assume~n_1=n_2~and~since~s_x^2>s_y^2~so~it~is~reasonable~to~see\\ F_{calc}>F_{0.05,n-1,n-1}.\\ From~table~we~see~that~F_{0.05,7,7}=3.79~and~F_{0.05,6,6}=4.28\\ so~minimum~no.~of~measurements~required~to~conclude~that~the~difference\\~in~standard~deviation~is~significant=7&plus;1=8$