A major issue facing many states is whether to legalize casino gambling.Suppose the governor of one state believes that more than 55% of the state's registered voters would favor some form of legal casino gambling.However,before backing a proposal to allow such gambling,the governor has instructed his aides to conduct a statistical test on the issue.To do this,the aides have hired a consulting firm to survey a simple random sample of 300 voters in the state.Of these 300 voters,175 actually favored legalized gambling. State the appropriate null and alternative hypotheses. A)H₀: p = 0.58 H_a: p ≠ 0.58 B)H₀: p ≤ 0.55 H_a: p 0.55 C)H₀: p = 0.55 H_a: p ≠ 0.55 D)H₀: p ≤ 0.58 H_a: p 0.58

Question

A major issue facing many states is whether to legalize casino gambling.Suppose the governor of one state believes that more than 55% of the state's registered voters would favor some form of legal casino gambling.However,before backing a proposal to allow such gambling,the governor has instructed his aides to conduct a statistical test on the issue.To do this,the aides have hired a consulting firm to survey a simple random sample of 300 voters in the state.Of these 300 voters,175 actually favored legalized gambling. State the appropriate null and alternative hypotheses. A)H₀: p = 0.58 H_a: p ≠ 0.58 B)H₀: p ≤ 0.55 H_a: p > 0.55 C)H₀: p = 0.55 H_a: p ≠ 0.55 D)H₀: p ≤ 0.58 H_a: p > 0.58

Quizplus · Accepted Answer

The appropriate null hypothesis would state that the true proportion of registered voters who favor legal casino gambling is less than or equal to 55% (HS1: p ≤ 0.55). The alternative hypothesis would state that the true proportion is greater than 55% (H1a: p > 0.55). This is because the governor believes that more than 55% of voters would favor legalized gambling and wants to test if the sample proportion of 175 out of 300 provides enough evidence to support this claim. The choice of B is the closest to this explanation.

A Major Issue Facing Many States Is Whether to Legalize