Question

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1,500 voting age citizens. 1,020 of the sampled citizens were in favor of an increase in cigarette 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 .66. Use α = 0.05.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.66

H_a : p > 0.66

n = 1500

x = 1020

= x / n = 1020 / 1500 = 0.68

P₀ = 0.66

1 - P₀ = 0.34

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.68 - 0.66 / [(0.66 * 0.34) / 1500]

= 1.15

Test statistic = 1.15

P(z > 1.15) = 1 - P(z < 1.15) = 0.1251

P-value = 0.1251

= 0.05

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence the proportion of citizens supporting an increase in cigarette taxes is significantly

greater than .66