In hypothesis testing, why can't the hypothesis be proved true?

Describe the four possible outcomes when conducting a hypothesis test.

According to a​ study, approximately​ 60% of US adults believe that they have​ achieved, or are within reach​ of, the​ "American Dream"​ (that is, home ownership and financial​ stability). Now consider a random sample of 400 US adults. What is the probablity that over​ 65% of the sampled adults believe they have reached or are optimistic about reaching the American​ Dream?    NEED ANSWER! No explanattion please

According to a New York Times/CBS News poll conducted during June 24–28, 2011, 55% of the American adults polled said that owning a home is a very important part of the American Dream (The New York Times, June 30, 2011). Suppose this result was true for the population of all American adults in 2011. In a recent poll of 1780 American adults, 60% said that owning a home is a very important part of the American Dream. Perform a hypothesis test to determine whether it is reasonable to conclude that the percentage of all American adults who currently hold this opinion is higher than 55%. Use a 10% significance level, and use both the p-value and the critical-value approaches. Round your answers for the observed value of z and the critical value of z to two decimal places, and the p-value to four decimal places.zobserved =Enter you answer; z_observed p-value =Enter you answer; p-value Critical value =Enter you answer; Critical value