Question

3. A product developer is investigating the tensile strength of a new synthetic fiber that will be used to make cloth for men's shirts. Strength is usually affected by the percentage of cotton used in the blend of materials for the fiber. The engineer conducts a completely randomized experiment with five levels of cotton content and replicated the experiment five times. The data are shown in the following table. Cotton Weight Percentage t Observations 15% 202 255 302 12HÌ 17 12Η | 18 | 18 | 1419 19 18 18H 19H | 25H| 22HÌ 19 | 23HİH 35h Is there evidence to support the claim that cotton content affects the mean tensile strength? Use a-0.05. Source df MS F- CV obs Cotton Percentage 475.76 14.76 Within/Error Total 636.96 24 What would be the null and alternate hypothesis in this study?lI Interpret your answer

Answer 1

Null hypothesis Ho: Cotton content does not affect the mean tensile strength Alternative hypothesis H: Cotton content affects the mean tensile strength Df for cotton percentages 5-1 4 Df for error 24-4 20 sum of squares for error= Total SS-cotton SS = 636.96-475.76-161.2 Mean SS for cotton SS for cotton/ df 475.76/4 118.94 Mean SS for error= SS for error/df = 161.2/20= 8.06 df Sum of Squares Mean Sum of F-statistic uares Source F critical value Cotton 4 475.76 118.94 14.76 2.87 ercentages Error Total 20 24 161.2 636.96 8.06 F critical value is taken from F-table at 4, 20 degrees of freedom at 0.05 level of significance Since F-calculated is greater than F-critical value, we reject the null hypothesis