To determine if a patient with a sore throat has a strep infection, a diagnostic test will have a positive outcome with a probability of 0.95 if the patient has strep, and it will have a negative outcome with a probability of 0.65 if the patient does not have strep. If 10% of the patients with a sore throat actually have a strep infection, what is the probability that a patient who gets a positive test actually has a strep infection?
Suppose that the manufacturer of Tan-Macle pearls produces pearls with a diameter that has a normal distribution with a mean of 0.52 cm and a standard deviation of 0.01 cm.
(a) What proportion of the manufactured pearls would have a diameter between 0.45 and 0.6 cm?
(b) What is the 64th percentile for this distribution?
Find z* for α = 0.07.
Explain how we know that is a "good" estimator for p.
Suppose that researchers are interested in determining what proportion of people are concerned about the environmental impacts of building a second nuclear power plant on Lake Anna. They took a random sample of 100 residents from communities around Lake Anna and found that 81% are concerned about the environmental impact of a second nuclear power plant.
(A) Find a 95% confidence interval for the proportion of residents who are concerned about the environmental impact of a second nuclear power plant.
(b) Explain what is meant by a 95% level of confidence.
A survey of 408 epidemiologists conducted during the Spring of 2020 (after the COVID-19 outbreak) indicated that 265 said they would wait over a year before they would attend a sporting event, concert, or play. Is this proportion more than 60%? Conduct the test using a 5% level of significance.