Justifying Claims: Confidence Interval, Population Proportion - AP Statistics
Card 1 of 30
What is the primary purpose of constructing a confidence interval?
What is the primary purpose of constructing a confidence interval?
Tap to reveal answer
To estimate a population parameter. Provides range of plausible values rather than single point.
To estimate a population parameter. Provides range of plausible values rather than single point.
← Didn't Know|Knew It →
Does a narrower confidence interval imply more or less variability in the data?
Does a narrower confidence interval imply more or less variability in the data?
Tap to reveal answer
Less variability. Narrower intervals indicate more precise estimates.
Less variability. Narrower intervals indicate more precise estimates.
← Didn't Know|Knew It →
What is the confidence interval interpretation if p is outside the interval?
What is the confidence interval interpretation if p is outside the interval?
Tap to reveal answer
The sample proportion is not consistent with p. Parameter value outside interval is not supported by data.
The sample proportion is not consistent with p. Parameter value outside interval is not supported by data.
← Didn't Know|Knew It →
For a 99% confidence interval, what is the z-score?
For a 99% confidence interval, what is the z-score?
Tap to reveal answer
$z = 2.576$. Captures the middle 99% of the standard normal distribution.
$z = 2.576$. Captures the middle 99% of the standard normal distribution.
← Didn't Know|Knew It →
Find and correct the error: 'A 90% confidence interval indicates a 90% chance the parameter is in the interval.'
Find and correct the error: 'A 90% confidence interval indicates a 90% chance the parameter is in the interval.'
Tap to reveal answer
Replace '90% chance' with '90% confidence'. Confidence refers to the method, not probability of specific interval.
Replace '90% chance' with '90% confidence'. Confidence refers to the method, not probability of specific interval.
← Didn't Know|Knew It →
Name one assumption necessary for a valid confidence interval for a proportion.
Name one assumption necessary for a valid confidence interval for a proportion.
Tap to reveal answer
Random sampling. Ensures representative sample for valid statistical inference.
Random sampling. Ensures representative sample for valid statistical inference.
← Didn't Know|Knew It →
What is the relationship between sample size and confidence interval width?
What is the relationship between sample size and confidence interval width?
Tap to reveal answer
Larger sample size, narrower interval. Inverse relationship: larger $n$ produces narrower intervals.
Larger sample size, narrower interval. Inverse relationship: larger $n$ produces narrower intervals.
← Didn't Know|Knew It →
How is a confidence interval used in hypothesis testing?
How is a confidence interval used in hypothesis testing?
Tap to reveal answer
To determine if the null value lies within the interval. If null value is in interval, fail to reject null hypothesis.
To determine if the null value lies within the interval. If null value is in interval, fail to reject null hypothesis.
← Didn't Know|Knew It →
What happens to the confidence interval if the confidence level decreases?
What happens to the confidence interval if the confidence level decreases?
Tap to reveal answer
It becomes narrower. Lower confidence level requires smaller critical value.
It becomes narrower. Lower confidence level requires smaller critical value.
← Didn't Know|Knew It →
What is the population proportion symbol?
What is the population proportion symbol?
Tap to reveal answer
$\text{p}$. Standard notation for the true population proportion parameter.
$\text{p}$. Standard notation for the true population proportion parameter.
← Didn't Know|Knew It →
If a confidence interval for a proportion is entirely above 0.5, what can be inferred?
If a confidence interval for a proportion is entirely above 0.5, what can be inferred?
Tap to reveal answer
The population proportion is likely greater than 0.5. All plausible values exceed 0.5, supporting majority claim.
The population proportion is likely greater than 0.5. All plausible values exceed 0.5, supporting majority claim.
← Didn't Know|Knew It →
What effect does a higher confidence level have on the confidence interval?
What effect does a higher confidence level have on the confidence interval?
Tap to reveal answer
It widens the interval. Higher confidence requires larger critical value, expanding interval.
It widens the interval. Higher confidence requires larger critical value, expanding interval.
← Didn't Know|Knew It →
If a confidence interval includes 0, what does this imply about the claim?
If a confidence interval includes 0, what does this imply about the claim?
Tap to reveal answer
The claim might not be true. Zero in the interval suggests no significant difference from null.
The claim might not be true. Zero in the interval suggests no significant difference from null.
← Didn't Know|Knew It →
Which distribution is used for constructing confidence intervals for proportions?
Which distribution is used for constructing confidence intervals for proportions?
Tap to reveal answer
Normal distribution. Assumes large sample size for central limit theorem to apply.
Normal distribution. Assumes large sample size for central limit theorem to apply.
← Didn't Know|Knew It →
What does the margin of error represent in a confidence interval?
What does the margin of error represent in a confidence interval?
Tap to reveal answer
The range of values above and below the sample statistic. Shows the maximum expected deviation from the point estimate.
The range of values above and below the sample statistic. Shows the maximum expected deviation from the point estimate.
← Didn't Know|Knew It →
What does it mean if a confidence interval is 0.1 to 0.4 for a proportion estimate?
What does it mean if a confidence interval is 0.1 to 0.4 for a proportion estimate?
Tap to reveal answer
The true proportion is likely between 0.1 and 0.4. Represents the range of plausible values for the true proportion.
The true proportion is likely between 0.1 and 0.4. Represents the range of plausible values for the true proportion.
← Didn't Know|Knew It →
What is the implication of a confidence interval that includes the null hypothesis value?
What is the implication of a confidence interval that includes the null hypothesis value?
Tap to reveal answer
Fail to reject the null hypothesis. Null value in interval means it's plausible given the data.
Fail to reject the null hypothesis. Null value in interval means it's plausible given the data.
← Didn't Know|Knew It →
What is the effect of increasing sample size on the margin of error?
What is the effect of increasing sample size on the margin of error?
Tap to reveal answer
Decreases the margin of error. Larger sample reduces variability and uncertainty.
Decreases the margin of error. Larger sample reduces variability and uncertainty.
← Didn't Know|Knew It →
Find and correct the error: 'The confidence interval is 0.5 to 0.8 with 100% certainty.'
Find and correct the error: 'The confidence interval is 0.5 to 0.8 with 100% certainty.'
Tap to reveal answer
Replace '100%' with the correct confidence level, e.g., 95%. Confidence intervals cannot provide 100% certainty.
Replace '100%' with the correct confidence level, e.g., 95%. Confidence intervals cannot provide 100% certainty.
← Didn't Know|Knew It →
Identify one potential issue with using a confidence interval for small samples.
Identify one potential issue with using a confidence interval for small samples.
Tap to reveal answer
The interval may be inaccurate. Small samples violate normality assumptions for proportion intervals.
The interval may be inaccurate. Small samples violate normality assumptions for proportion intervals.
← Didn't Know|Knew It →
Name one reason why a confidence interval might be preferred over a point estimate.
Name one reason why a confidence interval might be preferred over a point estimate.
Tap to reveal answer
It provides a range, indicating precision. Shows uncertainty and variability in the estimate.
It provides a range, indicating precision. Shows uncertainty and variability in the estimate.
← Didn't Know|Knew It →
What does it mean if a confidence interval is 0.1 to 0.4 for a proportion estimate?
What does it mean if a confidence interval is 0.1 to 0.4 for a proportion estimate?
Tap to reveal answer
The true proportion is likely between 0.1 and 0.4. Represents the range of plausible values for the true proportion.
The true proportion is likely between 0.1 and 0.4. Represents the range of plausible values for the true proportion.
← Didn't Know|Knew It →
If a confidence interval includes 0, what does this imply about the claim?
If a confidence interval includes 0, what does this imply about the claim?
Tap to reveal answer
The claim might not be true. Zero in the interval suggests no significant difference from null.
The claim might not be true. Zero in the interval suggests no significant difference from null.
← Didn't Know|Knew It →
For a 99% confidence interval, what is the z-score?
For a 99% confidence interval, what is the z-score?
Tap to reveal answer
$z = 2.576$. Captures the middle 99% of the standard normal distribution.
$z = 2.576$. Captures the middle 99% of the standard normal distribution.
← Didn't Know|Knew It →
What is the implication of a confidence interval that includes the null hypothesis value?
What is the implication of a confidence interval that includes the null hypothesis value?
Tap to reveal answer
Fail to reject the null hypothesis. Null value in interval means it's plausible given the data.
Fail to reject the null hypothesis. Null value in interval means it's plausible given the data.
← Didn't Know|Knew It →
What is the relationship between sample size and confidence interval width?
What is the relationship between sample size and confidence interval width?
Tap to reveal answer
Larger sample size, narrower interval. Inverse relationship: larger $n$ produces narrower intervals.
Larger sample size, narrower interval. Inverse relationship: larger $n$ produces narrower intervals.
← Didn't Know|Knew It →
Does a narrower confidence interval imply more or less variability in the data?
Does a narrower confidence interval imply more or less variability in the data?
Tap to reveal answer
Less variability. Narrower intervals indicate more precise estimates.
Less variability. Narrower intervals indicate more precise estimates.
← Didn't Know|Knew It →
If a confidence interval for a proportion is entirely above 0.5, what can be inferred?
If a confidence interval for a proportion is entirely above 0.5, what can be inferred?
Tap to reveal answer
The population proportion is likely greater than 0.5. All plausible values exceed 0.5, supporting majority claim.
The population proportion is likely greater than 0.5. All plausible values exceed 0.5, supporting majority claim.
← Didn't Know|Knew It →
Which distribution is used for constructing confidence intervals for proportions?
Which distribution is used for constructing confidence intervals for proportions?
Tap to reveal answer
Normal distribution. Assumes large sample size for central limit theorem to apply.
Normal distribution. Assumes large sample size for central limit theorem to apply.
← Didn't Know|Knew It →
What does the margin of error represent in a confidence interval?
What does the margin of error represent in a confidence interval?
Tap to reveal answer
The range of values above and below the sample statistic. Shows the maximum expected deviation from the point estimate.
The range of values above and below the sample statistic. Shows the maximum expected deviation from the point estimate.
← Didn't Know|Knew It →