Question

1. A mayor of a city wanted to know if the majority of residents supported a bill to outlaw smoking in any public setting. In a sample of 123 of the city’s residents 72 supported the ban. At the 5% significance level can it be claimed that the majority of the residents support the ban? To answer this be sure to formulate the appropriate hypotheses, calculate the test statistic, find the p-value and write your conclusion in the context of the problem.

Answer 1

H0: p = 0.5

Ha: p > 0.5

Sample proportion = 72 / 123 = 0.5854

Test statistics

z = - p / sqrt(p(1-p)/n)

= 0.5854 - 0.5 / sqrt( 0.5 * 0.5 / 123)

= 1.89

This is test statistics value.

p-value = P( Z > z)

= P( Z > 1.89)

= 1 - p( Z < 1.89)

= 1 - 0.9706

= 0.0294

Since p-value < 0.05 significance level, we have sufficient evidence to reject H0.

We conclude at 0.05 level that we have enough evidence to support the claim.