Cadmium a heavy metal is toxic to animals Mushrooms however

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 ppm. Below are cadmium levels for a random sample of the edible mushroom Boletus pinicoloa.

0.24

0.92

0.59

0.19

0.62

0.33

0.16

0.25

0.77

0.59

1.33

0.32

(a) Perform a hypothesis test at the 5% significance level to determine if the mean cadmium level in the population of Boletus pinicoloa mushrooms is greater than the government’s recommended limit of 0.5 ppm. Suppose that the standard deviation of this population’s cadmium levels is = 0.37 ppm. Note that the sum of the data is 6.31 ppm.

For this problem, be sure to: State your hypotheses, compute your test statistic, give the critical value and report your conclusion in terms of the original question.

(b) Find the p-value for the test.

(c) What assumptions are required for this test to be valid, i.e. to have true significance level of 5%?

(d) Suppose that in reality the true mean cadmium level in these mushrooms is µ =

0.57 ppm. Did your hypothesis test result in an error? If so, was it a Type I or Type II error? Explain.

Solution