t-TEST OF HYPOTHESIS ABOUT mu

TEST OF HYPOTHESIS ABOUT m

USING A T-SCORE

Certain types of mining operations release mildly radioactive byproducts. These byproducts may be released into the freshwater supply during the processing of ores. The EPA has issued a regulation that sets the maximum level for naturally occurring radiation in drinking water at 5 picocuries per liter. To see if a city’s water supply is safe, a random sample of 16 water specimens is selected, and the radiation in each specimen is measured in picocuries per liter. These data are below.

Using a = .01, is there sufficient evidence to indicate the mean level of radiation is safe (below the EPA’s maximum level)?

SOLUTION

The parameter of interest is m, the mean level of radiation in a city’s water supply.

Calculations from StatCrunch: t = -2.20, p-value = 0.022, not < .01 ---> Fail to Accept H_a

Interpretation: Testing at the .01 level of significance there is insufficient evidence to conclude that the mean level of radiation is less than 5 picocuries per liter. We cannot conclude the water is safe.

The complete StatCrunch analyses are below.

Hypothesis test results:
μ : mean of Variable
H₀ : μ = 5
H_A : μ < 5

Variable	Sample Mean	Std. Err.	DF	T-Stat	P-value
Radiation	4.644375	0.16181771	15	-2.1976888	0.022

A graph of the appropriate t-distribution and the resulting p-value is furnished below.