Question

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 2 in a thousand. Identify the type I error for the test.

A. Fail to reject the claim that the proportion of Americans that have seen a UFO is equal to 2 in a thousand when that proportion is actually less than 2 in a thousand.
B. Reject the claim that the proportion of Americans that have seen a UFO is equal to 2 in a thousand when that proportion is actually 2 in a thousand.
C. Reject the claim that the proportion of Americans that have seen a UFO is equal to 2 in a thousand when that proportion is actually less than 2 in a thousand.
D. Fail to reject the claim that the proportion of Americans that have seen a UFO is equal to 2 in a thousand when that proportion is actually greater than 2 in a thousand.

Answer 1

The correct option is (B).

Explanation:

A type-I-error occurs when we discard a true null-hypothesis (H₀).

The hypothesis in this case are:

H₀: The proportion of Americans that have seen a UFO is 0.002, i.e. p = 0.002.

Hₐ: The proportion of Americans that have seen a UFO is less than 0.002, i.e. p < 0.002.

A type I error will be committed, if we reject the claim that the proportion of Americans that have seen a UFO is equal to 2 in a thousand when that proportion is actually 2 in a thousand.

The correct option is (B).