Question

In the last election, a state representative received 52% of the votes cast. One year after the election, the representative organized a survey that asked a random sample of 300 people whether they would vote for him in the next election. If we assume that his popularity has not changed, what is the probability that more than half of the sample would vote for him?

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p > 0.5

n = 300

$\hat p$ = 0.52

P₀ = 0.5

1 - P₀ = 1 - 0.5 = 0.5

z = $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.52 - 0.5 / [$\sqrt$(0.5 * 0.5) / 300]

= 0.693

Test statistic = 0.693

This is the right tailed test .

P(z > 0.693) = 1 - P(z < 0.693) = 1 - 0.7558 = 0.2442

P-value = 0.2442

Probability = 0.2442