Researchers collected samples of water from streams in a mountain range to investigate the effects of acid rain. They measured the pH (acidity) of the water (a lower pH means the water is more acidic). They then classified the steams with respect to the kind of substrate (type of rock on which they flow). Here are the results:
Substrate Size Mean StandardDeviation Limestone 41 7.7 2.2
Shale 33 6.8 1.7
-Is there sufficient evidence that there is a significant difference in the acidity of streams that flow on limestone and on shale?
a. What is (are) the parameter(s) we are conducting inference on? Choose one of the following symbols (mean; meanDifferent (the mean difference from a matched pairs design); mean1 - mean2 (the mean difference from independent samples); p, or p1 – p2) and describe it in words.
b. Are the conditions satisfied? Why or why not?
If the answer to part b is no, do not complete the rest of #2.
c. At the 0.05 significance level, can the researcher conclude from these data that there is a significant difference between the mean acidity of the streams that flow on limestone and on shale?
i.State the null and alternative hypotheses.
ii.State the significance level for this problem.
iii.Calculate the test statistic.
iv.Calculate the P-value and include the probability notation statement.
v.State whether you reject or do not reject the null hypothesis.
vi.State your conclusion in context of the problem (i.e. interpret your results).
a. The parameter we are conducting inference on is the mean difference in acidity between streams that flow on limestone and streams that flow on shale.
b. To determine if the conditions are satisfied, we need to check if the samples are independent, the populations are approximately normal, and the populations have equal standard deviations. From the given information, it seems that the samples are independent since they are collected from different streams. However, we don't have information about the population's normality or the standard deviations. Therefore, we cannot determine if the conditions are satisfied.
c. Since we cannot determine if the conditions are satisfied, we cannot complete the rest of question 2.
In order to perform hypothesis testing, we need the sample means and sample standard deviations for both substrates. However, only the means and standard deviations for the substrate sizes are given, which is not relevant to the hypothesis test.