Question 1040329
A. Technically speaking, the alternative hypothesis would contain your claim, and would have to be either corroborated or resisted by the sample statistic. The null hypothesis states the status quo value, and would have to be retained or rejected based on later outcome.
CLAIM:  The population proportion p is less than 50%. (Because 13/50 = 0.26).
{{{H[0]: p = 0.50}}}
{{{H[a]: p < 0.50}}}


B. Level of significance = {{{alpha}}} = 0.10.

C. {{{z = (p[s] - p)/sqrt(p[s]*(1-p[s])/n)}}}, where {{{p[s]}}} is the sample proportion.
{{{z = (0.26 - 0.5)/sqrt(0.26*0.74/50) = -3.87}}}

D. P-value:  {{{P(z < = -3.87) = 0.0001}}}

E.  Since the p-value is much less than {{{alpha}}}, reject {{{H[0]}}}.

F.  The result suggests that the population proportion might be lower than the status quo value of 0.50.  A resampling with a bigger sample 
size might be necessary in order to confirm the result obtained above.