Question

a study was done on 1000 people to see if there is a difference between whether more men or women preferred cold or warmer weather. they found gender not to be dependent on the preference of weather. find the missing values for the females who chose cold or warmer weather.

gender and weather preference

\

$$\begin{tabular}{|l|l|l|l|} \\hline & cold weather & warm weather & total \\\\ \\hline male & 377 & 273 & 650 \\\\ \\hline female & & & 350 \\\\ \\hline total & & & 1000 \\\\ \\hline \\end{tabular}$$

147; 203
377; 273
175; 175
203; 147

Explanation:

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<reasoning>

Calculate the probability of weather preferences from the male data

\[

$$\begin{aligned} P(\text{Cold} \mid \text{Male}) &= \frac{377}{650} = 0.58 \\ P(\text{Warm} \mid \text{Male}) &= \frac{273}{650} = 0.42 \end{aligned}$$

\]

Apply independence condition to find female values

\[

$$\begin{aligned} \text{Female Cold} &= 350 \times 0.58 = 203 \\ \text{Female Warm} &= 350 \times 0.42 = 147 \end{aligned}$$

\]

Verify the total sum

\[
203 + 147 = 350
\]
</reasoning>

<answer>
<mcq-option>147; 203</mcq-option>
<mcq-option>377; 273</mcq-option>
<mcq-option>175; 175</mcq-option>
<mcq-correct>203; 147</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Statistics",
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]
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Answer:

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</pre_analysis>

<reasoning>

Calculate the probability of weather preferences from the male data

\[

$$\begin{aligned} P(\text{Cold} \mid \text{Male}) &= \frac{377}{650} = 0.58 \\ P(\text{Warm} \mid \text{Male}) &= \frac{273}{650} = 0.42 \end{aligned}$$

\]

Apply independence condition to find female values

\[

$$\begin{aligned} \text{Female Cold} &= 350 \times 0.58 = 203 \\ \text{Female Warm} &= 350 \times 0.42 = 147 \end{aligned}$$

\]

Verify the total sum

\[
203 + 147 = 350
\]
</reasoning>

<answer>
<mcq-option>147; 203</mcq-option>
<mcq-option>377; 273</mcq-option>
<mcq-option>175; 175</mcq-option>
<mcq-correct>203; 147</mcq-correct>
</answer>

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