Please explain to me and help me answer this question....?

Question

Concentration of total suspended sediment (TSS) were determined in A and B. The result (in mg/l) are as follows

A

21 38

31 50

42 57

33 41

28 39

45 37

B

63 57

92 96

103 107

95 82

81 99

121 89

Run an appropriate statistical test to show that the concentration of TSS in B is significantly higher than in A. Use a=0.05. What is your p value?

Do we assume the var is the same or the var is not the same? What is the solution for this question?

Please help me.....

Answer 1

ANSWER: There is statistically significant evidence that Sample B is different [higher] than Sample B.

Why???

TESTS BETWEEN TWO MEANS, POOLED T-TEST

1. Parameter of interest: μ1 = true average total suspended sediment (mg/l) in Sample A; μ2 = true average total suspended sediment (mg/l) in Sample B

2. Null hypothesis: H0 μ1 - μ2 = 0

3. Alternative hypothesis: Ha μ1 - μ2 < 0 (no difference in means)

4. Test statistic formula:  (see textbook)

A

AVE 38.5

SD 9.728122

B

AVE 90.41667

SD 17.90611

t-statistics; f

(Normal populations or n1 + n2 > 40) and independent observations and σ1 = σ2 and (σ1 and σ2 unknown)

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

5. Computation of t-test statistic and df values:

Two-Sample T-Test and CI

Sample   N   Mean  StDev  SE Mean

1       12  38.50   9.73      2.8

2       12   90.4   17.9      5.2

Difference = mu (1) - mu (2)

Estimate for difference:  -51.9167

90% upper bound for difference:  -44.0530

T-Test of difference = 0 (vs <): T-Value = -8.83  P-Value = 0.000  DF = 16

6. Determination of the P-value: The test is based  16 df. Table of t-DISTRIBUTION values shows area under 16 df curve to the right of T-Value = -8.83 is  area is 0.000 because of a “one-tailed” test

7. Conclusion: with significance value α = 0.05 (a reasonable level of significance) the above shows P-value < α [0.00 < 0.05], the Null hypothesis: H0 μ1 - μ2 = 0 should be rejected.  There is statistically significant evidence that Sample B is different [higher] than Sample B.