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.

Answer 1

Answer:

$H_0:p\leq0.55$

$H_a:p>0.55$

Step-by-step explanation:

Given : 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.

i.e. claim : $p>0.55$

Since alternative hypothesis shows there is statistical difference between the groups tested , it takes >, < or , ≠ sign.

Thus , the given claim is representing the alternative hypothesis :

$H_a:p>0.55$

Then, the null hypothesis will be (exactly opposite of alternative hypothesis ):

$H_0:p\leq0.55$

Thus , the appropriate null and alternative hypotheses.:

$H_0:p\leq0.55$

$H_a:p>0.55$