A dairy refuses to accept raw milk having more than 5000 bacteria per milliliter (mL). The bacteria count varies from shipment to shipment. Assume that the count of bacteria per milliliter is normally distributed with a population standard deviation of 14. The dairy wants to test that the mean bacteria count is less than 5000 per mL for the next shipment using a 5% significance level. A simple random sample of 62 one-mL samples from the next shipment resulted in a mean bacteria count of 4850. Use the information to perform a hypothesis test with a 0.05 significance level. In recent years, there has been increasing concern about the health effects of computer terminals. It is known that the miscarriage rate under general conditions is about 20%. A random sample of 697 pregnant women working with a computer 1 to 20 hours per week was taken. For this sample, there were 155 miscarriages. Test the claim that computer terminals detrimentally affect pregnant women with a 0.03 significance level using the traditional method.
Louis Pasteur had conducted a series of experiments that demonstrated the roles that yeast and bacteria play in the fermentation process. These results gave Joseph Lister, a British physician, the idea that human infections might have a similar organic origin. Lister developed a theory that using carbolic acid as a surgical room disinfectant would improve the postoperative survival rates for surgical patients. Out of the 50 patients amputated with the use of carbolic acid, 42 survived. Out of the 45 patients amputated without the use of carbolic acid, 23 survived. Test the claim that carbolic acid improved survival rates a using a 10% significance level.