Ships dumping garbage and ordinary beachgoers contribute to the increasing amount of trash that washes onto the shore and collects in the oceans all over the world. In 2012 the International Coastal Cleanup collected more than 9 million pounds of garbage from the world’s oceans. Common debris items collected included food wrappers, bottle caps, and beverage bottles. For the United States, cigarettes accounted for 28.1% of all debris items.26 A random sample of 430 debris items from a clean-up along a Texas beach was obtained.
a. Find the probability that the proportion of cigarette debris items is greater than 0.31.
b. Find the probability that the proportion of cigarette debris items is between 0.25 and 0.30.
c. Suppose 94 of the debris items are cigarettes. Is there any evidence to suggest that the true proportion of cigarette debris items is different from 0.281? Justify your answer.
Lowquality coffee shipped from various locations in Europe tends to contain a high proportion of defective beans (beans composed of foreign matter; moldy, black, unripe, or fermented beans; or those known as stinkers). Suppose a shipper claims the proportion of defective beans is 0.07. A U.S. packaging company receives a huge shipment of coffee beans and randomly select 1000 beans. If the sample proportion of defective beans is more than 0.09, then the entire shipment will be returned to the supplier in Europe.
a. If the true proportion of defective beans is 0.07 (as claimed), what is the probability that the shipment will be sent back?
b. If the true proportion of defective beans is 0.08, what is the probability that the shipment will be accepted?