Question

The pH factor is a measure of the acidity or alkalinity of water. A reading of 7.0 is neutral; values in excess of 7.0 indicate alkalinity; those below 7.0 imply acidity. Loren Hill states that the best chance of catching bass occurs when the pH of the water is in the range 7.5 to 7.9. Suppose you suspect that acid rain is lowering the pH of your favorite fishing spot and you wish to determine whether the pH is less than 7.5.

(a) State the alternative and null hypotheses that you would choose for a statistical test. (Choose Correct Letter)

a) H₀: μ < 7.5 versus H_a: μ > 7.5

b) H₀: μ = 7.5 versus H_a: μ > 7.5

c) H₀: μ ≠ 7.5 versus H_a: μ = 7.5

d) H₀: μ = 7.5 versus H_a: μ ≠ 7.5

e) H₀: μ = 7.5 versus H_a: μ < 7.5

(b) Does the alternative hypothesis in part (a) imply a one- or a two-tailed test? Explain. (Choose Correct Letter)

a) Since it is necessary to test that the average pH level is less than 7.5, the test is one-tailed.

b) Since it is necessary to test that the average pH level is more than 7.5, the test is one-tailed.    

c) Since it is necessary to test that the average pH level is different from 7.5, the test is two-tailed.

d) Since it is necessary to test that the average pH level is less than 7.5, the test is two-tailed.

e) Since it is necessary to test that the average pH level is different from 7.5, the test is one-tailed.

(c) Suppose that a random sample of 20 water specimens gave pH readings with x = 7.4 and s = 0.1. Just glancing at the data, do you think that the difference

x − 7.5 = −0.1 is large enough to indicate that the mean pH of the water samples is less than 7.5? (Do not conduct the test.)

Answer 1

(a) The given claim : The pH is less than 7.5 is represents the alternative hypothesis Ha.

Under H0 we assume the equality.

Therefore null and alternative hypothesis would be,

e) H0: μ = 7.5 versus Ha: μ < 7.5

(b) Since the alternative hypothesis consists of less than "<" sign , this is one left tail test.

a) Since it is necessary to test that the average pH level is less than 7.5, the test is one-tailed.

(c) Since n = 20 , it is small sample test and sample standard deviation s = 0.1 which is fairly smaller.

So the standard error of the sample mean would be enough smaller ,we are aslo given x bar = 7.4 which makes the test statistic larger and it results into significant evidence that mean pH of the water sample is less than 7.5