Question

This is a question for my stats class. Its a hypothesis problem with a conclusion.

In 2010, the mean pH level of rain in a county in northern New York was 5.38. A biologist believes that the rain acidity has changed. He takes a random sample of 30 rain dates in 2015 and obtains a acidity mean level of 5.34 with a standard deviation of 0.397. What is the conclusion: Has the acidity changed?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 5.38
Alternative Hypothesis, Ha: μ ≠ 5.38

Rejection Region
This is two tailed test, for α = 0.05 and df = 29
Critical value of t are -2.045 and 2.045.
Hence reject H0 if t < -2.045 or t > 2.045

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (5.34 - 5.38)/(0.397/sqrt(30))
t = -0.5519

P-value Approach
P-value = 0.5852
As P-value >= 0.05, fail to reject null hypothesis.

Acidity not changed