What does a confidence interval for a mean provide?
Select 2 correct answers:
A. An estimate of the population mean
B. The exact value of the population mean
C. A range of values likely to contain the population mean
D. The sample size used in the calculation
Answer (2)
A confidence interval provides an estimate of the population mean and a range of values likely to contain it. The correct options are A and C. It allows researchers to express uncertainty about their sample estimate of the population mean.
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A confidence interval for a mean provides important statistical information that helps us understand the estimation of the population mean from a sample. Here's how it works:
An estimate of the population mean (Option A): A confidence interval uses a sample mean to estimate the population mean. The sample mean is used as a point estimate, and the confidence interval provides a range around this estimate within which the true population mean is likely to lie.
A range of values likely to contain the population mean (Option C): This is the main feature of a confidence interval. It gives a range, calculated from the sample data, that is believed to cover the true population mean with a certain level of confidence (usually 95% or 99%). This means, for example, if you have a 95% confidence interval, you can say you are 95% confident that the interval contains the true population mean.
It's important to note that a confidence interval does not provide the exact value of the population mean (Option B). Instead, it suggests a range, and the true mean might or might not actually fall within this range. Additionally, while the sample size used in calculations (Option D) affects the width of the confidence interval (larger samples lead to narrower intervals), the confidence interval itself doesn't directly provide the sample size.
Overall, confidence intervals are a fundamental tool in statistics, allowing researchers to express how much uncertainty there might be in a sample estimate of a population parameter.
Therefore, the correct options for this question are (A) An estimate of the population mean, and (C) A range of values likely to contain the population mean.
