Draw Inferences From Random Samples - 7th Grade Math
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What is the sample size, written as $n$?
What is the sample size, written as $n$?
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The number of individuals or items in the sample. Sample size $n$ determines how many observations we collect.
The number of individuals or items in the sample. Sample size $n$ determines how many observations we collect.
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What is a parameter in this standard: population value or sample value?
What is a parameter in this standard: population value or sample value?
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Population value (the true but usually unknown value). Parameters are fixed but unknown; we estimate them using statistics.
Population value (the true but usually unknown value). Parameters are fixed but unknown; we estimate them using statistics.
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What is a statistic in this standard: population value or sample value?
What is a statistic in this standard: population value or sample value?
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Sample value (computed from the sample). Statistics are calculated from samples, parameters describe populations.
Sample value (computed from the sample). Statistics are calculated from samples, parameters describe populations.
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What does it mean for a sample to be random?
What does it mean for a sample to be random?
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Every member has an equal chance to be selected. Random selection ensures no systematic bias in choosing members.
Every member has an equal chance to be selected. Random selection ensures no systematic bias in choosing members.
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What is a sample in a sampling study?
What is a sample in a sampling study?
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A subset of the population that is actually measured. Samples are smaller groups used to make inferences about the whole population.
A subset of the population that is actually measured. Samples are smaller groups used to make inferences about the whole population.
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Which sample is more likely to give a stable estimate: $n=20$ or $n=200$?
Which sample is more likely to give a stable estimate: $n=20$ or $n=200$?
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$n=200$. Larger samples reduce sampling variability and give more stable estimates.
$n=200$. Larger samples reduce sampling variability and give more stable estimates.
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Identify the more likely biased method: survey first $30$ students entering school or random list?
Identify the more likely biased method: survey first $30$ students entering school or random list?
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Survey the first $30$ students entering school. Early arrivals may differ systematically from the whole population.
Survey the first $30$ students entering school. Early arrivals may differ systematically from the whole population.
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Find the range of sample means for $4.8,5.1,5.0,4.9$.
Find the range of sample means for $4.8,5.1,5.0,4.9$.
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$0.3$. Range = max - min = $5.1 - 4.8 = 0.3$.
$0.3$. Range = max - min = $5.1 - 4.8 = 0.3$.
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What is sampling variability?
What is sampling variability?
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Natural differences in estimates from different random samples. Different samples give different results due to chance alone.
Natural differences in estimates from different random samples. Different samples give different results due to chance alone.
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What is the sample mean word length if lengths are $4,5,3,8$?
What is the sample mean word length if lengths are $4,5,3,8$?
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$5$. Mean = $(4+5+3+8) div 4 = 20 div 4 = 5$.
$5$. Mean = $(4+5+3+8) div 4 = 20 div 4 = 5$.
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Identify the population: 50 students are randomly surveyed about school lunch.
Identify the population: 50 students are randomly surveyed about school lunch.
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All students at the school. The population is who we want to learn about, not just who we surveyed.
All students at the school. The population is who we want to learn about, not just who we surveyed.
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Identify the sample: 50 students are randomly surveyed about school lunch.
Identify the sample: 50 students are randomly surveyed about school lunch.
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The 50 surveyed students. The sample consists only of those actually surveyed.
The 50 surveyed students. The sample consists only of those actually surveyed.
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What is sampling bias?
What is sampling bias?
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A method that systematically favors certain outcomes. Bias leads to estimates that consistently miss the true value.
A method that systematically favors certain outcomes. Bias leads to estimates that consistently miss the true value.
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Which option describes an unbiased method: random sample or convenience sample?
Which option describes an unbiased method: random sample or convenience sample?
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Random sample. Random sampling gives each member equal selection probability.
Random sample. Random sampling gives each member equal selection probability.
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If repeated random samples of size $n$ give proportions from $0.46$ to $0.54$, what is a reasonable margin of error?
If repeated random samples of size $n$ give proportions from $0.46$ to $0.54$, what is a reasonable margin of error?
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About $0.04$. Margin of error ≈ half the range = $(0.54-0.46) div 2 = 0.04$.
About $0.04$. Margin of error ≈ half the range = $(0.54-0.46) div 2 = 0.04$.
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What is the population in a study that uses a sample to make an inference?
What is the population in a study that uses a sample to make an inference?
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The entire group of interest you want information about. The population includes everyone you want to study, not just the sample.
The entire group of interest you want information about. The population includes everyone you want to study, not just the sample.
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What is the population characteristic you are trying to estimate called?
What is the population characteristic you are trying to estimate called?
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A parameter (an unknown characteristic of the population). Parameters describe the entire population.
A parameter (an unknown characteristic of the population). Parameters describe the entire population.
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Which method best reduces bias: random sampling or choosing only volunteers?
Which method best reduces bias: random sampling or choosing only volunteers?
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Random sampling. Random selection gives everyone equal chance, reducing bias.
Random sampling. Random selection gives everyone equal chance, reducing bias.
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A random sample of $50$ students has $28$ who prefer pizza. What is the sample proportion $\hat{p}$?
A random sample of $50$ students has $28$ who prefer pizza. What is the sample proportion $\hat{p}$?
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$\hat{p}=\frac{28}{50}=0.56$. Divide favorable outcomes by total sample size.
$\hat{p}=\frac{28}{50}=0.56$. Divide favorable outcomes by total sample size.
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What is the formula for the mean of a sample with values $x_1, x_2, \dots, x_n$?
What is the formula for the mean of a sample with values $x_1, x_2, \dots, x_n$?
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$\bar{x}=\frac{x_1+x_2+\cdots+x_n}{n}$. Add all values and divide by count $n$.
$\bar{x}=\frac{x_1+x_2+\cdots+x_n}{n}$. Add all values and divide by count $n$.
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What is the main purpose of taking multiple random samples of the same size?
What is the main purpose of taking multiple random samples of the same size?
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To measure variability in the estimate from sample to sample. Multiple samples show how much estimates can vary.
To measure variability in the estimate from sample to sample. Multiple samples show how much estimates can vary.
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What is a simulation in the context of sampling?
What is a simulation in the context of sampling?
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A repeated random process used to imitate taking many samples. Simulations model real sampling without actual data collection.
A repeated random process used to imitate taking many samples. Simulations model real sampling without actual data collection.
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What happens to sampling variability when the sample size increases?
What happens to sampling variability when the sample size increases?
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It usually decreases. Larger samples give more stable estimates.
It usually decreases. Larger samples give more stable estimates.
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What is the sample statistic used to estimate a population characteristic called?
What is the sample statistic used to estimate a population characteristic called?
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An estimate (a sample statistic used to infer a population parameter). Sample statistics estimate population parameters.
An estimate (a sample statistic used to infer a population parameter). Sample statistics estimate population parameters.
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What does it mean if sample results vary a lot across repeated samples?
What does it mean if sample results vary a lot across repeated samples?
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The estimate is less reliable (high sampling variability). High variability means less confidence in the estimate.
The estimate is less reliable (high sampling variability). High variability means less confidence in the estimate.
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