Question: Two different companies (A and B) have applied to provide cable television service in a certain region. Let p denote the proportion of all potential subscribers who favor the company A over the company B based on a random sample of 25 individuals. Consider the case that company A wants to increase its production. Let the test statistic X be the number in the sample who favor the first company and x represent the observed value of X. What are the appropriate null and alternative hypotheses?
The answer is $H_0:p=0.5$, $H_a:p>0.5$
Where is $0.5$ coming from?
The null hypothesis is the hypothesis of no difference. In this case, no preference for either A or B or, equally likely to choose A or to choose B. Like tossing a fair coin, the probability of each choice is then $p=0.5$.
An alternative alternative hypothesis would be $p \neq 0.5$ and then let the evidence suggest if that corresponds to $p > 0.5$ or $p < 0.5$ .