# What are the null and alternative hypotheses in this phrase?

Suppose you work for a hotel chain and your boss makes the following claim: “I think that over 50 percent of hotels in large U.S. cities have a swimming pool.” Please test this claim using data from Tab3 and a 5-percent significance level.

The evidence is strong enough to reject the null hypothesis in favor of the alternative hypothesis… that is, your boss is “correct.” True or False?

The question, by my professor, states $$H_{a}:\mu>.5$$ and $$H_{o}:\mu<=.5$$. However, everything I read states it would be the opposite.

You want the null hypothesis to give you a probability distribution to work with, i.e., an exact value for $$\mu$$. So:

$$H_0: \mu=\frac12$$ $$H_a: \mu>\frac12$$

You could also say $$H_0: \mu\le\frac12$$ although it amounts to the same, if we say that the $$p$$-value is the greatest probability, that's consistent with $$H_0$$, that something as disfavorable to the null hypothesis should happen as did happen.