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Q. 4.18

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

Verified Solution

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.