Which is a correct interpretation?

Answer: We are 90% confident the population mean weight is between 4.2 and 4.8 kg. A confidence interval describes our confidence in capturing the population parameter, not individual values, probability, or future samples.

Which statement best describes the meaning of "95% confidence"?

Answer: About 95% of such intervals would capture the true population mean. Confidence level refers to the long-run capture rate of the procedure across repeated samples.

"We are 90% confident that μ is between 50 and 56" interprets a

Answer: 90% CI Standard CI interpretation.

AP Statistics · Topic 7.3

Justifying a Claim About a Population Mean Based on a Confidence Interval Practice

Part of Inference for Quantitative Data: Means.(UNC-4.F)

Practice questions

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Sample questions

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Sample 1difficulty 1/5
$A 90% confidence interval for the mean weight of adult salmon is (4.2, 4.8) kg.$
$Which is a correct interpretation?$
- A
  $We are 90% confident the population mean weight is between 4.2 and 4.8 kg.$
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- B
  $90% of samples will have a mean between 4.2 and 4.8 kg.$
- C
  $There is a 90% probability that the true mean is in this interval.$
- D
  $90% of adult salmon weigh between 4.2 and 4.8 kg.$
Why
$A confidence interval describes our confidence in capturing the population parameter, not individual values, probability, or future samples.$
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Sample 2difficulty 1/5
$A statistician constructs many 95% confidence intervals for a population mean using independent random samples.$
$Which statement best describes the meaning of "95% confidence"?$
- A
  $The probability that any one interval contains the mean is 0.95.$
- B
  $The sample mean lies in 95% of intervals.$
- C
  $About 95% of such intervals would capture the true population mean.$
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- D
  $95% of the data will fall within the interval.$
Why
$Confidence level refers to the long-run capture rate of the procedure across repeated samples.$
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Sample 3difficulty 3/5
$"We are 90% confident that μ is between 50 and 56" interprets a$
- A
  $Mean$
- B
  $90% CI$
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- C
  $Type I error$
- D
  $Significance level$
Why
$Standard CI interpretation.$
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Sample 4difficulty 3/5
$A 95% CI for mean reaction time of (240, 280) ms means$
- A
  $Mean is exactly 260 ms$
- B
  $95% of subjects respond between 240-280 ms$
- C
  $Reaction times average 95% accurate$
- D
  $We are 95% confident mean reaction time is between 240 and 280 ms$
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Why
$CI describes the parameter, not individual values.$
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Sample 5difficulty 3/5
$A 95% CI for μ is computed as (10.5, 13.5). The point estimate is$
- A
  $1.5$
- B
  $10.5$
- C
  $12.0$
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- D
  $13.5$
Why
$Midpoint = (10.5 + 13.5)/2 = 12.0.$
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