Question

It’s been found that 85% of American adults suffer from triskaidekaphobia (fear of the number 13). Researchers think this is too low and were interested to know if triskaidekaphobia has economic implications for large high-rise hotels. A USA Today/Gallup poll conducted February 9 – 11, 2007 asked 1,006 randomly selected people 18 years old and older in telephone interviews "Suppose you checked into a hotel and were given a room on the thirteenth floor. Would this bother you or not?" 87% of the survey respondents answered they would be bothered. Test the researchers’ claim at the 0.1 level of significance.

What are the correct null and alternative hypotheses?

Answer 1

Null Hypothesis,
`H_0` : p
`\leq` 85%

Alternate Hypothesis,
`H_A` : p > 85%

Explanation:

We are given that it's been found that 85% of American adults suffer from triskaidekaphobia (fear of the number 13).

A USA Today/Gallup poll asked 1,006 randomly selected people 18 years old and older in telephone interviews "Suppose you checked into a hotel and were given a room on the thirteenth floor. Would this bother you or not?" 87% of the survey respondents answered they would be bothered.

Let p = proportion of respondents who would be bothered about given a room on the thirteenth floor

SO, Null Hypothesis,
`H_0` : p
`\leq` 85%

Alternate Hypothesis,
`H_A` : p > 85%

Here, null hypothesis states that the proportion of respondents who would be bothered about given a room on the thirteenth floor is less than or equal to 85%.

On the other hand, alternate hypothesis states that the proportion of respondents who would be bothered about given a room on the thirteenth floor is more than 85%.

Hence, this would be the correct null and alternative hypothesis.