Question

Local environmentalists want to test if there is a difference in the pH of three different streams (called A, B, and C) feeding into Lake Travis. They took a random sample of 15 measurements from each stream and, after confirming all relevant assumptions, ran a one-way ANOVA on the data and got a significant (px0.05) result. 1. a. Write the appropriate null and altemative hypotheses for this analysis. (Ipt) b. List one potential confounding variable. (Ipt) c. In a post-hoc analysis, they got the following test statistics. Which pairs of streams have significantly different mean pH? Show work for full credit. (Bpt) Stream A vs. B: t-3.14 Stream B vs. C: t = 2.38 Stream A vs. C: t- 1.75

Answer 1

Local environmentalists want to test if there is a difference in the pH of three different streamsA, B and C.
They take random sample of size 15 from each stream.
Also they run one way ANOVA with level of significance 0.05.

a) Null and Alternative hypothesis.

$H_{0} : \mu_{1}=\mu_{2}=\mu_{3}$ Vs    at least one $\mu_{i}$ have significantly different mean.

c)
i)Stream A vs B:

Calculated value of t is -3.14
Critical value of t at 32 d.f. and 0.05 los is 2.0484
Since calculated |t| is greater than critical value.
hence stream A and B have significantly difference mean pH.

ii)Stream B vs C:
Calculated value of t is 2.38
Critical value of t at 32 d.f. and 0.05 los is 2.0484
Since calculated |t| is greater than critical value.
hence stream B and C have significantly difference mean pH.

ii)Stream A vs C:
Calculated value of t is 1.75
Critical value of t at 32 d.f. and 0.05 los is 2.0484
Since calculated |t| is greater than critical value.
hence stream A and C have no significantly difference mean pH.