Question

question 2
1 pts
a claim is made that 12% of adults do not have a drivers license. a researcher has reason to believe this claimed value is too high. after surveying a random sample of adults, the researcher observes that 8% of the adults in the sample do not have a drivers license. the researcher decides to conduct a hypothesis test and writes out the alternative hypothesis as ( h_{a}: p>0.12 ). what is wrong with this?
nothing is wrong.
the alternative hypothesis should be written as ( h_{a}: p = 0.08 ).
the alternative hypothesis should be written as ( h_{a}: p<0.12 ).
the alternative hypothesis should be written as ( h_{a}: p>0.08 ).
the alternative hypothesis should be written as ( h_{a}: p<12% ).

Explanation:

The null hypothesis \(H_0:p = 0.12\) (the claimed proportion). The researcher believes the claimed value is too high. So, the alternative hypothesis should be \(H_a:p<0.12\) (a one - sided test where we are looking for a proportion less than the claimed proportion). The sample proportion (\(0.08\)) is just an observation from the sample, and the alternative hypothesis is about the population proportion \(p\) (not directly about the sample proportion). Also, \(12\%=0.12\) and we should use the decimal form consistently in hypothesis testing.

Answer:

The alternative hypothesis should be written as \(H_a:p < 0.12\) and The alternative hypothesis should be written as \(H_a:p < 12\%\) (since \(12\% = 0.12\)).