Question

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes to help the public schools. The opinion poll recently sampled 1000 voting age citizens. 683 of the sampled citizens were in favor of an increase in taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than 65%.

What is the p-value?

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.65

H_a : p > 0.65

= x / n = 683 / 1000 = 0.683

P₀ = 0.65

1 - P₀ = 0.35

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.683 - 0.65 / [(0.65 * 0.35) / 1000]

= 2.188

= 2.19

P(z > 2.19) = 1 - P(z < 2.19) = 0.0143

P-value = 0.0143