a. Explain what it would mean to make a type I error.

Choose the correct answer below.

A.

A type I error would occur if in fact μ>0.56ppm, but the results of the sampling lead to the conclusion that μ=0.56 ppm.

B.A type I error would occur if in fact μ>0.56

ppm, but the results of the sampling fail to lead to the conclusion that μ=0.56 ppm.

C.A type I error would occur if in fact μ=0.56

ppm, but the results of the sampling lead to the conclusion that μ>0.56 ppm.

D.

A type I error would occur if in fact μ=0.56ppm, but the results of the sampling fail to lead to the conclusion that
μ>0.56 ppm.

Part 2

b. Explain what it would mean to make a type II error.

Choose the correct answer below.

A.

A type II error would occur if in fact μ>0.56ppm, but the results of the sampling fail to lead to the conclusion that
μ>0.56 ppm.

B. A type II error would occur if in fact μ>0.56

ppm, but the results of the sampling lead to the conclusion that μ>0.56 ppm.

C. A type II error would occur if in fact μ=0.56

ppm, but the results of the sampling lead to the conclusion that μ>0.56 ppm.

D.

A type II error would occur if in fact μ=0.56 ppm,
but the results of the sampling fail to lead to the conclusion that μ>0.56 ppm.

Part 3

c. Explain what it would mean to make a correct decision.

Choose the correct answer below.

A.

A correct decision would occur if μ=0.56ppm and the results of the sampling lead to the rejection of that fact; or if μ>0.56
ppm and the results of the sampling do not lead to that conclusion.

B.

A correct decision would occur if μ≠0.56ppm and the results of the sampling lead to the rejection of that fact; or if
μ=0.56 ppm and the results of the sampling do not lead to that conclusion.

C. A correct decision would occur if μ>0.56

ppm and the results of the sampling do not lead to the rejection of that fact; or if μ≠0.56
ppm and the results of the sampling lead to that conclusion.

D.

A correct decision would occur if μ=0.56ppm and the results of the sampling do not lead to the rejection of that fact; or if
μ>0.56
ppm and the results of the sampling lead to that conclusion.

Part 4

d. Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean cadmium level in that type of mushrooms equals the safety limit of 0.56 ppm.

Choose the correct answer below.

A.

type I error

B.

correct decision because a true null hypothesis is not rejected

C.

correct decision because a false null hypothesis is rejected

D.

type II error

Part 5

e. Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean cadmium level in that type of mushrooms exceeds the safety limit of 0.56 ppm.

Choose the correct answer below.

A.

type I error

B.

correct decision because a true null hypothesis is not rejected

C.

type II error

D.

correct decision because a false null hypothesis is rejected

Transcribed Image Text:Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. Some governments have a safety limit for cadmium in dry vegetables at 0.56 part per million (ppm). A research team measured the cadmium levels in a random sample of edible mushrooms, where the hypothesis test is to decide whether the mean cadmium level in the sample is greater than the governments' safety limit. The null and alternative hypotheses are Ho: μ = 0.56 ppm, H₂: μ> 0.56 ppm. Complete parts (a) through (e) below.

Question

a. Explain what it would mean to make a type I error.

Choose the correct answer below.

A.

A type I error would occur if in fact μ>0.56ppm, but the results of the sampling lead to the conclusion that μ=0.56 ppm.

B.A type I error would occur if in fact μ>0.56

ppm, but the results of the sampling fail to lead to the conclusion that μ=0.56 ppm.

C.A type I error would occur if in fact μ=0.56

ppm, but the results of the sampling lead to the conclusion that μ>0.56 ppm.

D.

A type I error would occur if in fact μ=0.56ppm, but the results of the sampling fail to lead to the conclusion that

μ>0.56 ppm.

Part 2

b. Explain what it would mean to make a type II error.

Choose the correct answer below.

A.

A type II error would occur if in fact μ>0.56ppm, but the results of the sampling fail to lead to the conclusion that

μ>0.56 ppm.

B. A type II error would occur if in fact μ>0.56

ppm, but the results of the sampling lead to the conclusion that μ>0.56 ppm.

C. A type II error would occur if in fact μ=0.56

ppm, but the results of the sampling lead to the conclusion that μ>0.56 ppm.

D.

A type II error would occur if in fact μ=0.56 ppm,
but the results of the sampling fail to lead to the conclusion that μ>0.56 ppm.

Part 3

c. Explain what it would mean to make a correct decision.

Choose the correct answer below.

A.

A correct decision would occur if μ=0.56ppm and the results of the sampling lead to the rejection of that fact; or if μ>0.56
ppm and the results of the sampling do not lead to that conclusion.

B.

A correct decision would occur if μ≠0.56ppm and the results of the sampling lead to the rejection of that fact; or if

μ=0.56 ppm and the results of the sampling do not lead to that conclusion.

C. A correct decision would occur if μ>0.56

ppm and the results of the sampling do not lead to the rejection of that fact; or if μ≠0.56
ppm and the results of the sampling lead to that conclusion.

D.

A correct decision would occur if μ=0.56ppm and the results of the sampling do not lead to the rejection of that fact; or if

μ>0.56

ppm and the results of the sampling lead to that conclusion.

Part 4

d. Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean cadmium level in that type of mushrooms equals the safety limit of 0.56 ppm.

Choose the correct answer below.

A.

type I error

B.

correct decision because a true null hypothesis is not rejected

C.

correct decision because a false null hypothesis is rejected

D.

type II error

Part 5

e. Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean cadmium level in that type of mushrooms exceeds the safety limit of 0.56 ppm.

Choose the correct answer below.

A.

type I error

B.

correct decision because a true null hypothesis is not rejected

C.

type II error

D.

correct decision because a false null hypothesis is rejected

Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. Some
governments have a safety limit for cadmium in dry vegetables at 0.56 part per million (ppm). A research team measured the cadmium levels in a random
sample of edible mushrooms, where the hypothesis test is to decide whether the mean cadmium level in the sample is greater than the governments'
safety limit. The null and alternative hypotheses are Ho: μ = 0.56 ppm, H₂: μ> 0.56 ppm. Complete parts (a) through (e) below.

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