Question 4.18: Tables 4.1 and 4.8 show results for two separate experiments...
Tables 4.1 and 4.8 show results for two separate experiments to determine the mass of a circulating U.S. penny. Determine whether there is a difference in the precisions of these analyses at α = 0.05.
| Table 4.1 Masses of Seven United States Pennies in Circulation | |
| Penny | Mass (g) |
| 1 | 3.080 |
| 2 | 3.094 |
| 3 | 3.107 |
| 4 | 3.056 |
| 5 | 3.112 |
| 6 | 3.174 |
| 7 | 3.198 |
| Table 4.8 Experimentally Determined Volumes Delivered by a 10-mL Class A Pipet | |||
| Trial | Volume Delivered (mL) | Trial | Volume Delivered (mL) |
| 1 | 10.002 | 6 | 9.983 |
| 2 | 9.993 | 7 | 9.991 |
| 3 | 9.984 | 8 | 9.990 |
| 4 | 9.996 | 9 | 9.988 |
| 5 | 9.989 | 10 | 9.999 |
Letting A represent the results in Table 4.1 and B represent the results in Table 4.8, we find that the variances are s^2_A = 0.00259 and s^2_B= 0.00138. A two-tailed significance test is used since there is no reason to suspect that the results for one analysis will be more precise than that of the other. The null and alternative hypotheses are
H_0: s_A^2 = s_B^2 H_A: s_A^2≠ s_B^2
and the test statistic is
F_{exp}=\frac{s_A ^2}{s_B^2} =\frac{0.00259}{0.00138}=1.88
The critical value for F(0.05, 6, 4) is 9.197. Since F_{exp} is less than F(0.05, 6, 4), the null hypothesis is retained. There is no evidence at the chosen significance level to suggest that the difference in precisions is significant.