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Question 1: Problem 5.109 from your text.  Do this problem by hand and scan/take a picture of your work and upload (You may also type your solution up)

Testing for HIV.

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.

Test Results

———————————————————————————————————————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) Draw a tree diagram for selecting a person from this population (outcomes: antibodies present or absent) and for testing his or her blood (outcomes: EIA positive or negative).

b) What is the probability that the EIA is positive for a randomly chosen person from this population?

P (test pos) = P (antibody and test pos) + P (no antibody and test pos.) =

(0.01)(0.9985)+ (0.99) (0.006) =0.016.

c) What is the probability that a person has the antibody, given that the EIA test is positive?

P (antibody | test pos) = P (antibody and test pos) = (0.01) (0.9985) = 0.624

P (test pos) 0.016

Question 2: Problem 5.110 from the text.  Do this problem by hand and scan/take a picture of your work and upload (You may also type your solution up)

Testing for HIV, continued.

The previous exercise gives data on the results of EIA test for the presence of antibodies to HIV. Repeat part (c) of that exercise for two different populations.

a) Blood donors are prescreened for HIV risk factors, so perhaps only 0.1% (0.001) of this population carries HIV antibodies.

b) Clients of a drug rehab clinic are a high risk group, so perhaps 10% of this population carries HIV antibodies.

c) What general lessons do your calculations illustrate?

Question 3:

Use the bitmap chart for the questions below

You will need to use both word and excel to complete this quiz.  Companies planning to introduce a new product in the market must define the “target” for the product.  Age and gender are two of the most important demographic variables.  The following two-way describes the age and marital status of American women in 1999.  The tables’ entries are in thousands of women.

 

Compute the marginal distribution of marital status for all adult women (use percents).  Use excel to create a bar chart to display this distribution.

Insert this graph into Word and discuss it.

Compare the conditional distributions of marital status for women aged 18 to 24 and women ages 40 to 64.  Discuss the most important difference between the two age groups.

Your company is planning a magazine aimed at women who have never been married.  Find the conditional distribution of age among never-married women and display it in a bar graph. Insert this graph into word.  Discuss what age group or groups you would suggest to your magazine to target.

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Book Name: The Pratice of Business Statistics Using Data for Decisions Author Moore, McCabe, Duckworth, and Alwan 2nd edition

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