Hypothesis testing without sample mean and standard deviation

Suppose we're looking at a two-candidate mayoral race in Providence. Candidate A is declared winner with 55 percent of the vote (p(hat) = 0.55). However, candidate B is suspicious of these results. Having his group of close friends take a random sample of 17 voters from Providence, he finds that 7 voted for candidate A while 10 voted for him.

On the basis of this study performed at the alpha = 0.05 level of significance, should candidate B demand a recount?

Formulate the null and alternative hypothesis and perform the test in order to respond to this question.

H0: u = 0.55

H1: u < 0.55 since p = 7/14 = 0.41

z = p(hat) - p / sqrt(p(1-p)/n) = 0.55 - 0.41 / sqrt(0.41(1-0.41)/17) = 1.17

p(z < 1.17) = 0.879 p(z > 1.17) = 1 - 0.879 = 0.121

Since 0.121 > 0.05, we don't reject the null hypothesis and candidate B shouldn't demand a recount.

Is this correct?