(d) Is random assignment to tents likely to ensure $\leq1~arachnophobe$ per tent?
- Random assignment and the independence assumption means that the answer to part c is the inverse of the outcome we're looking to avoid: $P(\gt1~arachnophobes) = 1-P(\leq1~arachnophobe)$. So, $P(\gt1~arachnophobes) = 1-0.84 = 0.16 = 16\%$. Those are the probabilities, but the interpretation really depends on how confident the camp counselor feels about a $16\%$ chance of having multiple arachnophobic campers in one of the tents.
+ Random assignment and the independence assumption means that the answer to part c is the complement of the outcome we're looking to avoid: $P(\gt1~arachnophobes) = 1-P(\leq1~arachnophobe)$. So, $P(\gt1~arachnophobes) = 1-0.84 = 0.16 = 16\%$. Those are the probabilities, but the interpretation really depends on how confident the camp counselor feels about a $16\%$ chance of having multiple arachnophobic campers in one of the tents.
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<li>Is random assignment to tents likely to ensure <span class="math inline">\(\leq1~arachnophobe\)</span> per tent?</li>
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-<p>Random assignment and the independence assumption means that the answer to part c is the inverse of the outcome we’re looking to avoid: <span class="math inline">\(P(\gt1~arachnophobes) = 1-P(\leq1~arachnophobe)\)</span>. So, <span class="math inline">\(P(\gt1~arachnophobes) = 1-0.84 = 0.16 = 16\%\)</span>. Those are the probabilities, but the interpretation really depends on how confident the camp counselor feels about a <span class="math inline">\(16\%\)</span> chance of having multiple arachnophobic campers in one of the tents.</p>
+<p>Random assignment and the independence assumption means that the answer to part c is the complement of the outcome we’re looking to avoid: <span class="math inline">\(P(\gt1~arachnophobes) = 1-P(\leq1~arachnophobe)\)</span>. So, <span class="math inline">\(P(\gt1~arachnophobes) = 1-0.84 = 0.16 = 16\%\)</span>. Those are the probabilities, but the interpretation really depends on how confident the camp counselor feels about a <span class="math inline">\(16\%\)</span> chance of having multiple arachnophobic campers in one of the tents.</p>
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