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Enzyme immunoassay (EIA) tests are used to screen blood specimens for the presence of antibodies to HIV, the virus that causes AIDS. Antibodies indicate the presence of the virus. The test is quite accurate but is not always correct. Here are approximate probabilities of positive and negative EIA outcomes when the blood tested does and does not actually contain antibodies to HIV. (Centers for Disease Control and Prevention, 1998.) Test Result + - Antibodies present 0.9985 0.0015 Antibodies absent 0.006 0.994 Suppose that 1% of a large population carries antibodies to HIV in their blood. a. Blood donors are prescreened for HIV risk factos, so perhaps only 0.1% (0.001) of this population carries HIV antibodies. Find the probability that a person from this population has the antibody given that the EIA test is positive. b. Clients of a drug rehab clinic are a high-risk group, so perhaps 10% of this population carries HIV antibodies. Find the probability that a person from this population has the antibody given that the EIA test is positive. c. What general lesson do your calculations illustrate?
Show the decision rule graphically. Use the .05 significance level.
Approximately 14 percent of the population of Arizona is 65 years or older. A random sample of five persons from this population is taken. The probability that less than 2 of the 5 are 65 years or older is:
In Meijer supermarket, the customer's waiting time to check out is approximately normally distributed with a standard deviation of 2.5 minutes.
What information would we need to test the claim that the difference in monthly benefits between the two groups is greater than $30 at the 0.05 level of significance? Write out the hypotheses and explain the testing procedure.
Creek Ratz is a very popular restaurant located along the coast of northern Florida. They serve a variety of steak and seafood dinners. During the summer beach season, they do not take reservations or accept a call seating.
Show all the steps of your hypothesis test including a) the claim being tested , b) the null and alternative hypothesis, c) the test statistic, d) the p value, e) initial conclusion, and f) a final conclusion about the original claim.
Develop a simple regression model that relates electricity usage to home size. What is the resulting regression equation?
If it rains in Greenville on Monday, there is a 80% chance that it will rain in NC that day. What is the probability it will rain in at least one of the above states.
Let denote the sample mean viewing time. What is the probability the sample mean will be within 0.25 hours of the population mean?
Find the area under the normal distribution curve to the right of z = -1.03.
Write a short paragraph explaining to the psychologist what can be concluded from this output (assuming the technical conditions are met).
Forecast quarterly demand where x = 0 in second quarter of last year. Quarterly seasonal factors are Q1=1.5, Q2=0.8, Q3=1.1, Q4=0.6. Determine the forecast for last quarter?
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