Question

What is our goal when constructing a confidence interval?

A. To estimate an unknown parameter.
B. To determine if there is bias in a sample.
C. To assess the presence of nonsampling error.
D. To determine if a sample is random.
E. To estimate an unknown statistic.

Answer 1

The goal when constructing a confidence interval is to estimate an unknown population parameter. A confidence interval provides a range of values that likely includes this parameter. It is constructed using the sample mean, error bound, and confidence level.

Step-by-step explanation:

The goal when constructing a confidence interval is to estimate an unknown population parameter. A confidence interval provides a range of values, calculated from the sample data, which is likely to contain the unknown parameter. Constructing a confidence interval involves several key steps:

• Finding the point estimate for the population mean.
• Calculating the error bound based on the desired confidence level and known standard deviation (if available).
• Creating the confidence interval by adding and subtracting the error bound to the point estimate.
• Interpreting the confidence interval in the context of the problem, acknowledging that if we took repeated samples, a certain percentage of the constructed confidence intervals would contain the true population parameter.

When constructing a confidence interval, the primary focus is not on determining bias in a sample, assessing non-sampling error, determining if a sample is random, or estimating an unknown statistic.