Question

Assume that a hypothesis test to support the given claim will be conducted. Identify the type l error for the test. A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 5 in a thousand. A. Fail to reject the claim that the proportion of Americans that have seen a UFO is equal to 5 in a thousand when that proportion is actually less than 5 in a thousand. B. Reject the claim that the proportion of Americans that have seen a UFO is equal to 5 in a thousand when that proportion is actually less than 5 in a thousand. C. Fail to reject the claim that the proportion of Americans that have seen a UFO is equal to 5 in a thousand when that proportion is actually greater than 5 in a thousand. D. Reject the claim that the proportion of Americans that have seen a UFO is equal to 5 in a thousand when that proportion is actually 5 in a thousand.

Answer 1

Option D) Reject the claim that the proportion of Americans that have seen a UFO is equal to 5 in a thousand when that proportion is actually 5 in a thousand.

Explanation:

We are given the following information:

A hypothesis test to support the given claim that the proportion of Americans that have seen a UFO is less than 5 in a thousand.

Type I error:

• Type I error is the rejection of a true null hypothesis that is we reject the null hypothesis given it is true.
• It is also known as a false positive.

First, we design the null and the alternate hypothesis

`H_(0): \text{ The proportion of Americans that have seen a UFO is equal to 5 in a thousand}\\H_A: \text{ The proportion of Americans that have seen a UFO is less than 5 in a thousand}`

Thus, for the given hypothesis test, we describe type I error as:

Option D) Reject the claim that the proportion of Americans that have seen a UFO is equal to 5 in a thousand when that proportion is actually 5 in a thousand.