Question

11. It is claimed that the approval rating of the government of a certain state is more than 50%. Out of a random sample of 300 people, 145 people gave the government a positive rating. Test the claim at ∝ = 0.05

Answer 1

Solution :

The null and alternative hypothesis is

H0 : p = 0.50

Ha : p > 0.50

= x / n = 145 / 300 = 0.4833

1 - P0 = 0.50

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.4833 - 0.50 / [(0.50 * 0.50) / 300]

z = -0.58

P-value = 0.7185

= 0.05

P-value >

Fail to reject the null hypothesis.

There is no sufficient evidence to support the claim.