An assistedliving home is an alternative to a nursing home and a bridge between a skilled-care facility and a patient’s residence. A recent report indicated 92% of all patients in assisted-living...

An assistedliving home is an alternative to a nursing home and a bridge between a skilled-care facility and a patient’s residence. A recent report indicated 92% of all patients in assisted-living homes are satisfied with the facility and the care. An insurance company believes that this percentage is actually much lower (due to health-care violations and strict for-profit motives). A random sample of 5000 patients in assisted-living homes around the country was obtained, and 4576 said they were satisfied with the facility and the care.

a. Is there any evidence to suggest the true proportion of assisted-living patients who are satisfied is less than 0.92? Use a = 0.01.

b. Find the p value associated with this hypothesis test.

c. Carefully sketch a graph illustrating the critical value, value of the test statistic, and p value.