The maximum acceptable level of a certain toxic chemical in vegetables has been

Question

The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.4 parts per million (ppm). A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer to determine whether the mean level of the chemical in these tomatoes exceeds the recommended limit. The hypotheses are H0: ? ? 0.4 ppm Ha: ? > 0.4 ppm where ? is the mean level of the chemical in tomatoes from this producer. Explain the meaning of a Type I error.

A Type I error would occur if, in fact, ? > 0.4 ppm, but the results of the sampling fail to lead to that conclusion.

A Type I error would occur if, in fact, ? ? 0.4 ppm, but the results of the sampling lead to the conclusion that ? > 0.4 ppm

A Type I error would occur if, in fact, ? ? 0.4 ppm, but the results of the sampling fail to lead to rejection of that fact.

A Type I error would occur if, in fact, ? > 0.4 ppm, and the results of the sampling lead to rejection of the null hypothesis that ? ? 0.4 ppm.

Explanation / Answer

Given that, null and alternative hypotheses are,

H0: ? ? 0.4 ppm Versus Ha: ? > 0.4 ppm

Type I error: Reject the null hypothesis(H0) , when in fact it is true.

Therefore in above case type I error is,

Type I error would occur if, in fact, ? ? 0.4 ppm, but the results of the sampling lead to the conclusion that ? > 0.4 ppm

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.