Question

Lead concentrations in drinking water should always be below the EPA action level of 15 parts per million. Named so for if levels exceed this amount, then the EPA recommends actions be taken to investigate and reduce the amount of lead found in the water source. To ensure safety, water sources are periodically tested for lead concentration levels. What would it mean for such a test to result in a type II error?

Answer 1

for this test null hypothesis is

Mean EPA action level is 15 ppm

alternative hypothesis is

Mean EPA action level is < 15 ppm

Type II error:

type II error occurs when we fail to reject the false null hypothesis. which means null hypothesis is false but still we do not reject it.

in this case,

Type II error means, actually mean EPA action level is bellow 15 ppm, but we reject this true fact and say that the mean EPA action level is greater than or equal to 15 ppm.

Note: (ppm = parts per million)