Question

​Cadmium, a heavy​ metal, is toxic to animals.​ Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. A government set a safety limit for cadmium in dry vegetables at 0.5 parts per million​ (ppm). The cadmium levels in a random sample of one species of edible mushroom are in the accompanying data set. At the ​10 % significance​ level, do the data provide sufficient evidence to conclude that the mean cadmium level in this species of mushroom is greater than the​ government's recommended limit of ​0.5 ppm? Assume that the population standard deviation of cadmium levels in this species of mushroom is 0.37 ppm. Preliminary data analyses indicate that applying the​ z-test is reasonable.​ (Note: The sum of the data is 6.32 ​ppm.)

State the hypotheses for the​ one-mean z-test. ​:

Compute the value of the test statistic. z nothing ​(Round to two decimal places as​ needed.)

Determine the critical​ value(s).

Answer 1

Hypothesis are

The critical value for the right tailed test is

Rejection region Z>1.2816

Test statistic :

where

is the sample mean

Sum of the data is 6.32

if n = 10

sample mean is

Test statistic :

Rejection Region : Z>1.2816

Test statistic do not lie in the rejection region, hence we fail to reject the null hypothesis.

Hence the data do not provide sufficient evidence to conclude that the mean cadmium level in this species of mushroom is greater than the​ government's recommended limit of ​0.5 ppm