Q. 9.15 - Elementary Statistics

Question

Cadmium, a heavy metal, is toxic to animals. Mushrooms, however are able to absorb and accumulate cadmium at high concentrations. The Czech and Slovak governments have set a safety limit for cadmium in dry vegetables at \(0.5\) part per million M. Melgar et al. measured the cadmium levels in a random sample of the edible mushroom Boletus pinicola and published the results in the paper "Influence of Some Factors in Toxicity and Accumulation of Cd from Edible Wild Macrofungi in NW Spain. A hypothesis test is to be performed to decide whether the mean cadmium level in Boletus pinicola mushrooms is greater than the government's recommended limit. 

a. determine the null hypothesis

b. determine the alternative hypothesis

c. classify the hypothesis test as two tailed, left tailed or right tailed.

Step-by-Step Solution

Answer

Part a. \(H_{0}:\mu =0.5\) ppm

Part b. \(H_{0}:\mu >0.5\) ppm

Part c. The hypothesis is a right tailed test.

Part a. Step 1. Explanation

Here the null hypothesis is the mean of cadmium level in Boletus pinicola mushrooms equal to \(0.5\) ppm.

\(H_{0}:\mu =0.5\) ppm 

Part b. Step 1. Explanation

Here the alternative hypothesis is the mean of cadmium level in Boletus pinicola mushrooms greater to  \(0.5\) ppm.

\(H_{0}:\mu >0.5\) ppm

Part c. Step 1.

As the alternative hypothesis is preferred that is mean of cadmium level in Boletus pinicola mushrooms greater to \(0.5\) ppm so, this is right tailed test.