Measurement and Data>Using Random Samples to Make Inferences About Populations(TEKS.Math.7.12.B)
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Texas 7th Grade Math › Measurement and Data>Using Random Samples to Make Inferences About Populations(TEKS.Math.7.12.B)
In a random survey of 120 voters in a city, 45% said they support a new policy. What is the best inference about all voters in the city?
About 45% of all voters likely support the policy, but the actual percent could be somewhat different.
Exactly 45% of all voters support the policy.
The sample proves the policy will pass because almost half support it.
You can only infer about those 120 voters, not the whole city.
Explanation
A random sample supports a population inference. The estimate is $\hat{p}=0.45$. It suggests the population proportion is near 45%, but sampling variability means the true value could be a bit higher or lower. It does not prove an exact percent or guarantee an election outcome.
A park ranger randomly surveys 200 visitors and finds that 58 arrived by bike. The park expects 15,000 visitors this month. Which statement is the best population inference?
Exactly 58 of the 15,000 visitors will arrive by bike.
About 29% of visitors (around 4,350 out of 15,000) may arrive by bike, recognizing the true percent could differ a bit.
At least half of visitors will arrive by bike because 58 is close to 100.
You cannot make any inference because 200 is too small to be useful.
Explanation
From the random sample, $\hat{p}=\frac{58}{200}=0.29$. Applying this rate to 15,000 gives $0.29\times 15{,}000\approx4{,}350$. This is an estimate with uncertainty; the actual percent could be somewhat higher or lower due to sampling variability.