Populations, Samples, and Random Selection SAT Practice

MathChapter 8: Statistics

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Question 1 of 50

Question 1

Easy

Question 11 of 50

Question 11

Easy

Which evaluation best fits displayed sampling plan \(1\)?

Proposed sampling plan
Plan
A principal surveys the first \(40\) students entering one door.

The method is automatically a census.The sample size alone guarantees no bias.Convenience sample; arrival location may omit many students.The plan proves a causal effect.

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Question 12 of 50

Question 12

Easy

Which evaluation best fits displayed sampling plan \(2\)?

Proposed sampling plan
Plan
A city posts an optional poll on its website.

The method is automatically a census.The sample size alone guarantees no bias.The plan proves a causal effect.Voluntary response; residents with stronger opinions may reply more often.

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Question 13 of 50

Question 13

Easy

Which evaluation best fits displayed sampling plan \(3\)?

Proposed sampling plan
Plan
A computer randomly selects IDs from a complete membership list.

Random selection; the chance mechanism supports representativeness.The method is automatically a census.The sample size alone guarantees no bias.The plan proves a causal effect.

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Question 14 of 50

Question 14

Easy

Which evaluation best fits displayed sampling plan \(4\)?

Proposed sampling plan
Plan
A store asks only customers buying one premium product.

The method is automatically a census.Selection bias; the sample excludes other customer types.The sample size alone guarantees no bias.The plan proves a causal effect.

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Question 15 of 50

Question 15

Easy

Which evaluation best fits displayed sampling plan \(5\)?

Proposed sampling plan
Plan
A transit survey is conducted only at noon on one route.

The method is automatically a census.The sample size alone guarantees no bias.Time-and-location undercoverage; it may not represent all riders.The plan proves a causal effect.

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Question 16 of 50

Question 16

Medium

Which evaluation best fits displayed sampling plan \(6\)?

Proposed sampling plan
Plan
Every tenth randomly ordered record is selected after a random start.

The method is automatically a census.The sample size alone guarantees no bias.The plan proves a causal effect.A chance-based systematic method with broad coverage.

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Question 17 of 50

Question 17

Medium

Which evaluation best fits displayed sampling plan \(7\)?

Proposed sampling plan
Plan
A coach chooses the athletes who attend optional extra practice.

Convenience and self-selection concerns.The method is automatically a census.The sample size alone guarantees no bias.The plan proves a causal effect.

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Question 18 of 50

Question 18

Medium

Which evaluation best fits displayed sampling plan \(8\)?

Proposed sampling plan
Plan
Names are drawn from all registered voters using a random-number generator.

The method is automatically a census.Random selection from the target sampling frame.The sample size alone guarantees no bias.The plan proves a causal effect.

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Question 19 of 50

Question 19

Medium

Which evaluation best fits displayed sampling plan \(9\)?

Proposed sampling plan
Plan
A restaurant surveys only people who use its delivery app.

The method is automatically a census.The sample size alone guarantees no bias.Undercoverage of dine-in and phone-order customers.The plan proves a causal effect.

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Question 20 of 50

Question 20

Medium

Which evaluation best fits displayed sampling plan \(10\)?

Proposed sampling plan
Plan
A school emails everyone but analyzes only voluntary replies.

The method is automatically a census.The sample size alone guarantees no bias.The plan proves a causal effect.Nonresponse or voluntary-response bias may remain.

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Question 21 of 50

Question 21

Medium

Using random-sample summary \(1\), about how many population members are estimated to have the characteristic?

Random-sample summary
Sample size \(n\)	With characteristic \(x\)	Population size \(N\)
\(40\)	\(12\)	\(2000\)

\(600\)\(24000\)\(50\)\(640\)

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Question 22 of 50

Question 22

Medium

Using random-sample summary \(2\), about how many population members are estimated to have the characteristic?

Random-sample summary
Sample size \(n\)	With characteristic \(x\)	Population size \(N\)
\(80\)	\(22\)	\(3200\)

\(70400\)\(880\)\(40\)\(960\)

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Question 23 of 50

Question 23

Medium

Using random-sample summary \(3\), about how many population members are estimated to have the characteristic?

Random-sample summary
Sample size \(n\)	With characteristic \(x\)	Population size \(N\)
\(150\)	\(42\)	\(2500\)

\(105000\)\(17\)\(700\)\(850\)

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Question 24 of 50

Question 24

Medium

Using random-sample summary \(4\), about how many population members are estimated to have the characteristic?

Random-sample summary
Sample size \(n\)	With characteristic \(x\)	Population size \(N\)
\(240\)	\(66\)	\(1600\)

\(105600\)\(7\)\(680\)\(440\)

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Question 25 of 50

Question 25

Medium

Using random-sample summary \(5\), about how many population members are estimated to have the characteristic?

Random-sample summary
Sample size \(n\)	With characteristic \(x\)	Population size \(N\)
\(125\)	\(45\)	\(900\)

\(324\)\(40500\)\(7\)\(449\)

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Question 26 of 50

Question 26

Medium

Using random-sample summary \(6\), about how many population members are estimated to have the characteristic?

Random-sample summary
Sample size \(n\)	With characteristic \(x\)	Population size \(N\)
\(300\)	\(81\)	\(5000\)

\(405000\)\(1350\)\(17\)\(1650\)

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Question 27 of 50

Question 27

Medium

Using random-sample summary \(7\), about how many population members are estimated to have the characteristic?

Random-sample summary
Sample size \(n\)	With characteristic \(x\)	Population size \(N\)
\(64\)	\(20\)	\(1200\)

\(24000\)\(19\)\(375\)\(439\)

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Question 28 of 50

Question 28

Medium

Using random-sample summary \(8\), about how many population members are estimated to have the characteristic?

Random-sample summary
Sample size \(n\)	With characteristic \(x\)	Population size \(N\)
\(180\)	\(63\)	\(2400\)

\(151200\)\(13\)\(1020\)\(840\)

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Question 29 of 50

Question 29

Medium

Using random-sample summary \(9\), about how many population members are estimated to have the characteristic?

Random-sample summary
Sample size \(n\)	With characteristic \(x\)	Population size \(N\)
\(250\)	\(95\)	\(4000\)

\(1520\)\(380000\)\(16\)\(1770\)

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Question 30 of 50

Question 30

Medium

Using random-sample summary \(10\), about how many population members are estimated to have the characteristic?

Random-sample summary
Sample size \(n\)	With characteristic \(x\)	Population size \(N\)
\(500\)	\(135\)	\(12000\)

\(1620000\)\(3240\)\(24\)\(3740\)

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Question 31 of 50

Question 31

Medium

Two random samples use the same method; sizes are \(80\) and \(800\). Which generally has less sampling variability?

Reliability consideration
Question
Two random samples use the same method; sizes are \(80\) and \(800\). Which generally has less sampling variability?

The opposite conclusion is always true.Population size is the only factor.The sample of \(800\).Any sample is exact if arithmetic is correct.

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Question 32 of 50

Question 32

Medium

A biased convenience sample grows from \(100\) to \(10{,}000\). What remains unresolved?

Reliability consideration
Question
A biased convenience sample grows from \(100\) to \(10{,}000\). What remains unresolved?

The opposite conclusion is always true.Population size is the only factor.Any sample is exact if arithmetic is correct.The systematic selection bias.

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Question 33 of 50

Question 33

Medium

Random samples of size \(300\) are taken from populations of \(100{,}000\) and \(1{,}000{,}000\). At this source level, which is most reasonable?

Reliability consideration
Question
Random samples of size \(300\) are taken from populations of \(100{,}000\) and \(1{,}000{,}000\). At this source level, which is most reasonable?

Their reliability can be broadly similar when selection quality is the same.The opposite conclusion is always true.Population size is the only factor.Any sample is exact if arithmetic is correct.

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Question 34 of 50

Question 34

Medium

Why can two good random samples give different proportions?

Reliability consideration
Question
Why can two good random samples give different proportions?

The opposite conclusion is always true.Sampling variability.Population size is the only factor.Any sample is exact if arithmetic is correct.

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Question 35 of 50

Question 35

Medium

Which improvement best addresses undercoverage?

Reliability consideration
Question
Which improvement best addresses undercoverage?

The opposite conclusion is always true.Population size is the only factor.Expand the sampling frame so omitted population groups can be selected.Any sample is exact if arithmetic is correct.

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Question 36 of 50

Question 36

Medium

Which improvement mainly reduces random sampling variability?

Reliability consideration
Question
Which improvement mainly reduces random sampling variability?

The opposite conclusion is always true.Population size is the only factor.Any sample is exact if arithmetic is correct.Increase the size of a properly selected random sample.

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Question 37 of 50

Question 37

Medium

Does sampling \(10\%\) of one population and \(1\%\) of another automatically make the first result better?

Reliability consideration
Question
Does sampling \(10\%\) of one population and \(1\%\) of another automatically make the first result better?

No; sample size and selection quality matter more directly here.The opposite conclusion is always true.Population size is the only factor.Any sample is exact if arithmetic is correct.

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Question 38 of 50

Question 38

Medium

A large online poll accepts anyone who clicks. What is the main limitation?

Reliability consideration
Question
A large online poll accepts anyone who clicks. What is the main limitation?

The opposite conclusion is always true.Voluntary responders may differ systematically from nonresponders.Population size is the only factor.Any sample is exact if arithmetic is correct.

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Question 39 of 50

Question 39

Medium

A random sample proportion changes slightly on repetition. Is that evidence of failure?

Reliability consideration
Question
A random sample proportion changes slightly on repetition. Is that evidence of failure?

The opposite conclusion is always true.Population size is the only factor.No; chance variation among samples is expected.Any sample is exact if arithmetic is correct.

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Question 40 of 50

Question 40

Medium

Which statement about sample size is best?

Reliability consideration
Question
Which statement about sample size is best?

The opposite conclusion is always true.Population size is the only factor.Any sample is exact if arithmetic is correct.Larger random samples generally stabilize estimates but cannot guarantee exactness.

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Question 41 of 50

Question 41

Hard

A random sample gives \(\hat{p}=0.42\) with a stated margin of \(0.04\). Which interval is represented?

Inference scenario
Scenario
A random sample gives \(\hat{p}=0.42\) with a stated margin of \(0.04\). Which interval is represented?

\(0.38\) to \(0.46\)The exact opposite statement.Sample size alone answers the question.No population definition is needed.

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Question 42 of 50

Question 42

Hard

A sample proportion is \(0.30\) for population size \(8{,}000\). What is the estimated count?

Inference scenario
Scenario
A sample proportion is \(0.30\) for population size \(8{,}000\). What is the estimated count?

The exact opposite statement.\(2{,}400\)Sample size alone answers the question.No population definition is needed.

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Question 43 of 50

Question 43

Hard

A survey result from only honors classes is used to describe all students. What is the central problem?

Inference scenario
Scenario
A survey result from only honors classes is used to describe all students. What is the central problem?

The exact opposite statement.Sample size alone answers the question.The sample may not represent the target population.No population definition is needed.

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Question 44 of 50

Question 44

Hard

Two random samples have the same size, but one omits rural members from its frame. Which is better supported?

Inference scenario
Scenario
Two random samples have the same size, but one omits rural members from its frame. Which is better supported?

The exact opposite statement.Sample size alone answers the question.No population definition is needed.The sample whose frame includes the whole target population.

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Question 45 of 50

Question 45

Hard

A sample of \(400\) has \(156\) successes. What proportion and estimated count for \(5{,}000\) are correct?

Inference scenario
Scenario
A sample of \(400\) has \(156\) successes. What proportion and estimated count for \(5{,}000\) are correct?

\(0.39\) and \(1{,}950\)The exact opposite statement.Sample size alone answers the question.No population definition is needed.

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Question 46 of 50

Question 46

Hard

Why is ‘about \(1{,}950\)’ better than ‘exactly \(1{,}950\)’ for a scaled sample result?

Inference scenario
Scenario
Why is ‘about \(1{,}950\)’ better than ‘exactly \(1{,}950\)’ for a scaled sample result?

The exact opposite statement.It acknowledges sampling variability.Sample size alone answers the question.No population definition is needed.

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Question 47 of 50

Question 47

Hard

A voluntary poll has \(50{,}000\) responses. What conclusion is safest?

Inference scenario
Scenario
A voluntary poll has \(50{,}000\) responses. What conclusion is safest?

The exact opposite statement.Sample size alone answers the question.Its large size does not remove voluntary-response bias.No population definition is needed.

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Question 48 of 50

Question 48

Hard

A study defines its population as customers who purchased this month. Can it generalize automatically to all residents?

Inference scenario
Scenario
A study defines its population as customers who purchased this month. Can it generalize automatically to all residents?

The exact opposite statement.Sample size alone answers the question.No population definition is needed.No; the target populations differ.

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Question 49 of 50

Question 49

Hard

Which symbolic expression estimates a population count?

Inference scenario
Scenario
Which symbolic expression estimates a population count?

\((x/n)N\)The exact opposite statement.Sample size alone answers the question.No population definition is needed.

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Question 50 of 50

Question 50

Hard

What distinction resolves ambiguous use of ‘population parameter’ in a sample estimate?

Inference scenario
Scenario
What distinction resolves ambiguous use of ‘population parameter’ in a sample estimate?

The exact opposite statement.The parameter belongs to the population; the sample statistic estimates it.Sample size alone answers the question.No population definition is needed.

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Question 34Sample size and reliability
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Question 35Sample size and reliability
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Question 36Sample size and reliability
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Question 37Sample size and reliability
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Question 38Sample size and reliability
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Question 39Sample size and reliability
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Question 40Sample size and reliability
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Question 41Advanced sampling inference
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Question 42Advanced sampling inference
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Question 43Advanced sampling inference
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Question 44Advanced sampling inference
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Question 45Advanced sampling inference
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Question 46Advanced sampling inference
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Question 47Advanced sampling inference
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Question 48Advanced sampling inference
Hard
Question 49Advanced sampling inference
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Question 50Advanced sampling inference
Hard

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