3. An HIV test is not entirely accurate. The test developer claims the test producesless than 5% false positives and less than 1% false negatives. In order toinvestigate the developer's claim, the test was administered to1000 individualsknown to have HIV and 10,000 individuals known not to have HIV. The results arebelow.Truly has HIVTruly does notTest Resulthave HIVPositive993591Negative79409

Question
Asked Nov 21, 2019
1 views

(a) Construct a 95% confidence interval for the proportion of false positives 
produced by the test. 

3. An HIV test is not entirely accurate. The test developer claims the test produces
less than 5% false positives and less than 1% false negatives. In order to
investigate the developer's claim, the test was administered to1000 individuals
known to have HIV and 10,000 individuals known not to have HIV. The results are
below.
Truly has HIV
Truly does not
Test Result
have HIV
Positive
993
591
Negative
7
9409
help_outline

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3. An HIV test is not entirely accurate. The test developer claims the test produces less than 5% false positives and less than 1% false negatives. In order to investigate the developer's claim, the test was administered to1000 individuals known to have HIV and 10,000 individuals known not to have HIV. The results are below. Truly has HIV Truly does not Test Result have HIV Positive 993 591 Negative 7 9409

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Expert Answer

Step 1

Step-by-step procedure to obtain the value of  using STATKEY:

  • Choose Normal under Theoretical Distributions.
  • In Normal Distribution, click Edit Parameters.
  • Enter mean as 0 and standard deviation as 1 and click Ok.
  • Click the Centre Proportion value in graph and enter 95.
  • Click Two-Tail.
  • Click OK.

Output using the MINITAB software is given below:

Normal Distribution
Reset Plot
Left Tail
Two-TailRight Tail
0.40
0.35
0.30
0.25
0.20
0.025
0.950
0.025
0.15
0.10
0.05
0.00
-4.0
-2b
1.0
-3.0
1.0
0.0
1.0
3.0
4.0
-1.960
1.960
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Normal Distribution Reset Plot Left Tail Two-TailRight Tail 0.40 0.35 0.30 0.25 0.20 0.025 0.950 0.025 0.15 0.10 0.05 0.00 -4.0 -2b 1.0 -3.0 1.0 0.0 1.0 3.0 4.0 -1.960 1.960

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Step 2

From the output, the value of  is 1.96 for 95% confidence.

Here, the number of false positives 
produced by the test is 591 and the total number of positive test result is 1,584.

The sample proportion is,

p=
п
591
1,584
-0.373
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p= п 591 1,584 -0.373

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Step 3

The 95% confidence interval i...

P1-p)
Sample statistic tz* SE = ptz*.,
п
0.373(1-0.373)
= 0.373±1.96,
1,584
=0.373 0.024
=(0.349,0.397)
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P1-p) Sample statistic tz* SE = ptz*., п 0.373(1-0.373) = 0.373±1.96, 1,584 =0.373 0.024 =(0.349,0.397)

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Hypothesis Testing

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