Question

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. 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. 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. 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. 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. 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.

Answer 1

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.

Explanation:

We are given that a hypothesis test of the given claim is conducted. A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 2 in a thousand.

Let p = the proportion of Americans that have seen a UFO

So, Null Hypothesis,
`H_0` : p =
`(2)/(1000)` = 0.002

Alternate Hypothesis,
`H_A` : p <
`(2)/(1000)` ⇒ p < 0.002

Here, the null hypothesis states that the proportion of Americans that have seen a UFO is equal to 2 in a thousand.

On the other hand, the alternate hypothesis states that the proportion of Americans that have seen a UFO is less than 2 in a thousand.

Now, the type I error states that the probability of rejecting the null hypothesis given the fact that the null hypothesis is true. Or, it is the probability of rejecting a true hypothesis.

So, in this context, the type I error is 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 2 in a thousand.