Members of the homeowners\' association (HOA) want to know whether a majority of
ID: 3052815 • Letter: M
Question
Members of the homeowners' association (HOA) want to know whether a majority of homeowners from a local residential community support a 2% annual increase in HOA fees for five years to fund the resurfacing of the community swimming pool. To investigate, they survey a random sample of 50 homeowners and use the results to test the hypotheses H0: p = 0.50 and Ha: p > 0.50, where p is the proportion of all homeowners who support a 2% annual increase in HOA fees for five years to fund the pool resurfacing. In the context of this study, how could a Type I error occur?
a. The HOA finds convincing evidence that a majority of homeowners do not support the fee increase, when in reality there isn't convincing evidence that a majority supports the increase.
b. The HOA finds convincing evidence that a majority of homeowners support the fee increase, when in reality, at most, 50% of the homeowners support the increase.
c. The HOA finds convincing evidence that a majority of homeowners support the fee increase, when in reality more than 50% of the homeowners do support the increase.
d. The HOA does not find convincing evidence that a majority of homeowners support the fee increase, when in reality more than 50% of the homeowners do support the increase.
e. The HOA does not find convincing evidence that a majority of homeowners support the fee increase, when in reality, at most, 50% of the homeowners do support the increase.
Explanation / Answer
as type I error is to rjeect null hypothesis when in relatiy it is not to be rejected.
hence option B is correct
b. The HOA finds convincing evidence that a majority of homeowners support the fee increase, when in reality, at most, 50% of the homeowners support the increase.