According to the American Veterinary Medical Foundation, $30.4\%$ of U. S. households owned at least one cat in 2012. Josephina wonders if this percentage is currently true for households in her town. To investigate, she contacts randomly selected households in her town and determines the proportion of these households that own at least one cat. To analyze the results of her study she will use a one sample $z$-test for proportions.
Which of the following is a condition that must be satisfied in order for her test to be valid?