Question

The U.S. Department of Agriculture provided homogenized baby food samples to three labs for analysis.3 Results agreed well for protein, fat, zinc, riboflavin, and palmitic acid. Results for iron were questionable: Lab A, 1.59 ± 0.14 (13); Lab B, 1.65 ± 0.56 (8); Lab C, 2.68 ± 0.78 (3) mg/100 g. Uncertainty is the standard deviation, with the number of replicate analyses in parentheses. Use two separate t tests to compare results from Lab C with those from Lab A and Lab B at the 95% confidence level. Comment on the sensibility of the t test results. Offer your own conclusions.

 

 

Answer 1

wo-Sample T-Test and CI

 

Sample N    Mean    StDev    SE Mean
1       13    1.590     0.140      0.039
2        3     2.680     0.780       0.45

Difference = μ (1) - μ (2)
Estimate for difference: -1.090
95% CI for difference: (-1.532, -0.648)
T-Test of difference = 0 (vs ≠): T-Value = -5.28 P-Value = 0.000 DF = 14

 

Both use Pooled StDev = 0.3220

Lab B - 1 and Lab C - 2

Two-Sample T-Test and CI

 

Sample    N    Mean    StDev    SE Mean
1          8     1.650     0.560  0.20
2         3      2.680    0.780  0.45

Difference = μ (1) - μ (2)
Estimate for difference: -1.030
95% CI for difference: (-1.973, -0.087)
T-Test of difference = 0 (vs ≠): T-Value = -2.47 P-Value = 0.036 DF = 9

Both use Pooled StDev = 0.6157

wo-Sample T-Test and CI

 

Sample N    Mean    StDev    SE Mean
1       13    1.590     0.140      0.039
2        3     2.680     0.780       0.45