Probability or Statistics In each of the following problems, identify the population and the sample, and determine whether the question involves probability or statistics.
a. Seventy-five percent of all people who buy a dining room table purchase matching chairs. Five people who purchased a dining room table within the last month are selected at random. What is the probability that all five purchased matching chairs?
b. Twenty-five people entering a rest area and food court on Highway 59 near Houston are selected at random. Of these 25 people, 20 purchased food from at least one of the eateries. Estimate the true proportion of people stopping at this rest area who purchase food.
c. Historical records indicate 1 out of every 500 people using a particularly steep water slide suffer some kind of injury. Fifty people using the slide are selected at random. How many do you expect to be injured?
d. A building inspector in Henderson, Nevada, is checking public buildings with doors that open automatically. One hundred doors are randomly selected. Careful inspection reveals that 12 doors are broken. Use this information to estimate the percentage of automatic doors in Henderson that are broken.
e. One thousand people entering Los Angeles International Airport (LAX) are selected at random. Each person is asked to complete a short survey regarding travel. The survey results show 637 carry a frequent-flier card. Is there evidence to suggest the true proportion of travelers entering LAX who carry frequent flier cards is greater than 0.60?
f. The Risdall Advertising Agency reports 65% of all women have purchased perfume within the last three months. Thirty-four women are selected at random. Is it likely more than 20 of these women purchased perfume within the last three months?
g. Representatives from the Occupational Safety and Health Administration inspected several for-profit and Medicare nursing homes for any violations. The resulting data will be used to determine whether there is any evidence to suggest the quality of treatment is different in the two types of nursing homes.