Question

Elevated phosphate levels in lakes and rivers can cause algal blooms and other problems. To protect these ecosystems, several strict pollution laws were enacted. Prior to these laws, the phosphate levels in a river had a true mean and variance of 650 μg/l and 640, respectively. After the laws were enacted, 12 water samples were found to have a sample mean of 500 μg/l. Assuming phosphate levels are normally distributed, perform a hypothesis test at α = 0.05 to see if phosphate levels were reduced after the laws were enacted.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 650
Alternative Hypothesis, Ha: μ < 650

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (500 - 650)/(640/sqrt(12))
z = -0.81

P-value Approach
P-value = 0.209
As P-value >= 0.05, fail to reject null hypothesis.

The phosphate levels were not decreased.