Following an oil spill, a particular region of the ocean is being tested for the

Question

Following an oil spill, a particular region of the ocean is being tested for the level of a chemical called naphthalene. It is considered fact that fish from the region will be safe to eat if, and only if, the mean naphthalene level in the region is less than 3.3 parts per billion. A set of water specimens will be randomly selected from the region and tested, and if the results provide convincing evidence that the mean naphthalene level is less than 3.3, then the sale of fish from the region will be made legal. Which of the following describes a Type I error and its consequences? (A) The authorities obtain convincing evidence that the mean naphthalene level is less than 3.3, and legalize the sale of fish that are in fact safe for consumption. (B) The authorities obtain convincing evidence that the mean naphthalene level is less than 3.3, and legalize the sale of fish that are in fact unsafe for consumption. (C) The authorities fail to obtain convincing evidence that the mean naphthalene level is less than 3.3, and do not legalize the sale of fish from the region when in fact the fish are safe for consumption. (D) The authorities fail to obtain convincing evidence that the mean naphthalene level is less than 3.3, and do not legalize the sale of fish from the region when in fact the fish are unsafe for consumption. (E) The definition of a Type I error depends on the actual results of the study in question.

Explanation / Answer

Type I error is defined as,

Type I error = P(reject H0 / H0 is true)

Reject H0 means accept H1

Here H1 (alternative hypothesis is mean naphthalene level in the region is less than 3.3 parts per billion.

Type I error can be written in word as the authorities obtain convincing evidence that the mean naphthalene level in the region is less than 3.3 parts per billion and legalize the sale of fish that are in fact safe for consumption.

Here option A) is correct.

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