Question

Problem 5: An exit poll from an election was taken with 1024 random voters. 528 voters favored the incumbent. Is the race too close to call? Use Hypothesis testing with 1% level of significance to answer the question. Hint: What is the probability of a candidate winning if the race is “too close to call”?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p 0.5

= x / n = 528 / 1024 = 0.5156

P₀ = 0.5

1 - P₀ = 0.5

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.5156 - 0.5 / [(0.5 * 0.5) / 1024]

= 1

P(z > 1) = 1 - P(z < 1) = 0.1587

P-value = 0.3174

= 0.01

P-value >

Fail to reject the null hypothesis .

There is no sufficient evidence to conclude that  the race too close to call .