Confidence Levels in Analytical Chemistry?

Question

The following results were reported for two samples. In each case determine:

1. report the uncertainty of the result at the 95% confidence level.

2. determine if the calcium content of the two tablets is significantly different at the 95% confidence level using the t-test.

Sample12: 14.31, 15.36, 15.55, 15.85 wgt-% Ca

Sample48: 15.13, 15.14, 10.83, 15.35 wgt-% Ca

***Remember to consider the deletion of outliers with the q-test.

(I figured the mean to be 15.27 and the standard deviation to be 0.67 for sample12 and 14.11 and 2.19 for sample48.

Please help me, I've read and re-read the chapters and cannot understand the equations at all. Please show steps wherever possible. Or at least take me through it step-by-step.

Answer 1

ANSWER: CALCIUM CONTENT between Sample 12 and Sample 48 are not significantly different.

Why??

TESTS BETWEEN TWO MEANS, UNPOOLED T-TEST

1. Parameters of interest:

μ12 = true average of POPULATION 12 wgt-% Ca CALCUM CONTENT

μ48 = true average of POPULATION 48 wgt-% Ca CALCUM CONTENT

2. Null hypothesis: H0 μ12 - μ48 = 0

3. Alternative hypothesis: Ha μ12 - μ48 ≠ 0 ("two-tailed" test requirement for "significantly different")

4. Test statistic formulae: (Two-sample unpooled t-test)

"t" value and "df" value

http://en.wikipedia.org/wiki/Statistical...

5. Computation of test statistic and df values

[Sample48 individual "outlier" = 10.83 deleted]

SUMMARIZED DATA

Sample  N    Mean  StDev  

12       4  15.268  0.669     0.33

48       3  15.207  0.124    0.072

Two-Sample T-Test and CI

Difference = mu (1) - mu (2)

Estimate for difference:  0.060830

95% CI for difference:  (-1.028589, 1.150249)

T-Test of difference = 0 (vs not =): T-Value = 0.18  P-Value = 0.870  DF = 3

6. Determination of the P-value: The test is based on 3 df Table "Look-up" shows area under 3 df curve "two-tailed"

is 0.870. Because P-value >  ÃŽÂ±  (=1 - 0.95)/2 [0.870 > 0.025] Null Hypothesis cannot be rejected.  Null Hypothesis of no difference between CALCIUM CONTENT of Sample 12 and Sample 48 cannot be rejected at a confidence level of 95%. CALCIUM CONTENT between Sample 12 and Sample 48 are not significantly different.