A political party claims that it will obtain more than 30% of the vote in a forthcoming by-election. An opinion survey of 1000 voters indicates 400 will vote for the party. Assess the governing party's claim at a 5% significance level.

(a) State the hypotheses. Write the meaning of the hypotheses.

(b) Compute the associated standardized statistic and corresponding p-value.

(c) Find the critical value.

(d) Indicate the conclusions of your test in terms of the problem.