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 1% 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 0.39 ppm. Preliminary data analyses indicate that applying the z-test is reasonable. (Note: The sum of the data is 6.76 ppm.) State the hypotheses for the one-mean z-test. H0: μ = 0.5 ppm Ha: μ > 0.5 ppm Compute the value of the test statistic. z=0.56 (Round to two decimal places as needed.) Determine the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) A. The critical value is zα=2.33 B. The critical values are ±zα/2=±____________ C. The critical value is −zα=___________ ________________ (Reject or Do Not Reject) the null hypothesis. At the 1% significance level, the data ____________ (do not provide or provide) sufficient evidence to conclude that the mean cadmium level is ___________ (less than, equal to, not the same as, more than) the government's recommended limit.
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 1% 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 0.39 ppm. Preliminary data analyses indicate that applying the z-test is reasonable. (Note: The sum of the data is 6.76 ppm.) State the hypotheses for the one-mean z-test. H0: μ = 0.5 ppm Ha: μ > 0.5 ppm Compute the value of the test statistic. z=0.56 (Round to two decimal places as needed.) Determine the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) A. The critical value is zα=2.33 B. The critical values are ±zα/2=±____________ C. The critical value is −zα=___________ ________________ (Reject or Do Not Reject) the null hypothesis. At the 1% significance level, the data ____________ (do not provide or provide) sufficient evidence to conclude that the mean cadmium level is ___________ (less than, equal to, not the same as, more than) the government's recommended limit.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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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 1% 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 0.39 ppm. Preliminary data analyses indicate that applying the z-test is reasonable. (Note: The sum of the data is 6.76 ppm.)
State the hypotheses for the one-mean z-test.
H0: μ = 0.5 ppm
Ha: μ > 0.5 ppm
Compute the value of the test statistic.
z=0.56
(Round to two decimal places as needed.)
Determine the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.)
________________ (Reject or Do Not Reject) the null hypothesis. At the
1% significance level, the data ____________ (do not provide or provide) sufficient evidence to conclude that the mean cadmium level is ___________ (less than, equal to, not the same as, more than) the government's recommended limit.
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