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 Ha : p ≠ 0.58
B) H0 : p ≤ 0.55 Ha : p 0.55
C) H0 : p = 0.55 Ha : p ≠ 0.55
D) H0 : p ≤ 0.58 Ha : 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 Ha : p ≠ 0.58
B) H0 : p ≤ 0.55 Ha : p > 0.55
C) H0 : p = 0.55 Ha : p ≠ 0.55
D) H0 : p ≤ 0.58 Ha : p > 0.58

Quizplus · Accepted Answer

The null hypothesis (H0) typically represents a statement of no effect or no difference, or a statement of equality, and it is what we assume to be true before we collect data. The alternative hypothesis (Ha) is what we want to have enough evidence to support and usually represents a new claim or the effect we suspect might be true. Since the governor believes that more than 55% of the voters would favor legalized gambling, the null hypothesis should reflect the scenario of 55% or less (p ≤ 0.55), and the alternative should reflect the scenario of more than 55% (p > 0.55).

A Major Issue Facing Many States Is Whether to Legalize