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@Planeshifter
Last active August 19, 2020 17:41
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Use HTML lists <ol> (ordered list), <ul> (unordered list), and <li> (list item)
<ol>
<li>The output below pertains to the participants in the Fast Food experiment. It reports summary statistics for the variable “dieting” by the respondent’s self-identified race. Variable “dieting” is coded as 1 if the respondent reported he/she was dieting, and 0 if the respondent reported no. From this table, calculate the probability that a randomly chosen participant in this experiment is dieting. Show the basis for your calculation and perform this calculation with relevant probabilities calculated to the thousandth (e.g, 0.342, 0.096, 0.004). (Note: You’ll observe that the top row constituing 22 respondents reports no race. Do not include this group in your calculation.)
<Image src="https://isle.heinz.cmu.edu/95-796_Module3c_Q1.jpg" alt="Homework 2 Question 1 Image" />
</li>
<li>This problem concerns testing for COVID19 antibodies.
Let:
$C^{+}$ denote actually having COVID19 antibodies (i.e. “ground truth”) <br />
$\tilde{C}^{+}$ denote not actually having COVID19 antibodies (i.e. “ground truth”)<br />
$T^{+}$ denote testing + for COVID19 antibodies
For the Rapid COVID19 test:
$$ P(T^{+} | C^{+}) = 0.96 $$
$$ P(T^{+} | \tilde{C}^{+}) = 0.06 $$
<ul>
<li>Suppose $P(C^{+})$ = 0.01, what is $P(C^{+} |T^{+})$?</li>
<li>Suppose instead that$P(C^{+})$ = 0.1, what then is $P(C^{+} |T^{+})$?</li>
<li>Why does $P(C^{+} |T^{+})$? change so much between a) and b)?</li>
</ul>
</li>
</ol>
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