Question

A student in wildlife management studied trout habitat in the upper Shavers Fork watershed in West Virginia. The springtime water pH of 29 randomly selected tributary sample sites were found to have the following values:
6.2 6.3 5.0 5.8 4.6 4.7 4.7 5.4 6.2 6.0 5.4 5.9 6.2 6.1 6.0 6.3 6.2 5.8 6.2 6.3 6.3 6.3 6.4 6.5 6.6 6.1 6.3 4.4 6.7
Do the data of Exercise 17.8 (above) give good reason to think that the springtime water the tributary water basin around the Shavers Fork watershed is not neutral. (A neutral pH is the pH of pure water, pH 7.)
Step 1:
STATE: Is there evidence that the springtime water pH of the Shavers Fork watershed is not neutral (pH 7)?
FORMULATE: State hypotheses to be tested.
A. H 0 : μ = 7 vs. Ha : μ > 7
B. H 0 : μ = 7 vs. Ha : μ < 7
C. H 0 : μ = 7 vs. Ha : μ ≠ 7
D. H 0 : μ ≠ 7 vs. Ha : μ < 7

Answer 1

Answer:

C. H 0 : μ = 7 vs. Ha : μ ≠ 7

Since the calculated value of t = -9.462 falls in the critical region  t ≤-2.048

We conclude that the  springtime water the tributary water basin around the Shavers Fork watershed is not neutral. We accept our alternate hypothesis and reject the null hypothesis.

Step-by-step explanation:

The null hypothesis the usually the test to be performed. Here we want to check whether the water is neutral or not. Neutral water must have a pH of 7 . This can be stated as the null hypothesis. And the claim is treated as the alternate hypothesis that water in not neutral or not having pH= 7

In symbols it will be written as

H0: : μ = 7 vs. Ha : μ ≠ 7

So choice C is the best option for this hypothesis testing.

Let the significance level be 0.05

The degrees of freedom = n-1= 29-1 = 28

The critical value is  t ≥ 2.048 and t ≤ - 2.048 for 0.05 two tailed test with 28 df.

The test statistic to use is t- test

t= x- u/ s/√n

The total sum is 170.9 and mean = x= 5.893

The u = 7

And the sample standard deviation is =s= 0.63

Putting the values

t= 5.893-7/0.63/√29

t= - 1.107/0.11699

t= -9.4623

Since the calculated value of t = -9.462 falls in the critical region  t ≤-2.048

We conclude that the  springtime water the tributary water basin around the Shavers Fork watershed is not neutral. We accept our alternate hypothesis and reject the null hypothesis.