Question to test your Introduction to Confidence Intervals knowledge

Question

A quality control engineer collected a simple random sample of 10 bolts produced in a batch to assess their lengths (in millimeters). The sample has the following statistics:

Sample mean $open paren x overline close paren equals 24.07 mm$

Margin of error (ME) for a $90 percent sign$ confidence interval $equals 0.11 mm$

Construct the $90 percent sign$ confidence interval for the true mean length of bolts produced in the first batch using the given statistics. Another confidence interval for a sample of bolts from a second batch is reported as $open paren 23.95 mm comma 24.25 mm close paren$ . How does the result compare to the confidence interval of the second batch? Explain possible reasons for differences in their widths.

Accepted Answer

The interval is $open paren 23.96 mm comma 24.18 mm close paren$ ; the second interval is wider, likely due to higher variability or smaller sample size.

Answer

The interval is $open paren 23.96 mm comma 24.18 mm close paren$ ; both intervals are equal in width due to equal sample sizes.

Answer

The interval is $open paren 23.96 mm comma 24.18 mm close paren$ ; the second interval is wider due to a lower confidence level.

Answer

The interval is $open paren 23.96 mm comma 24.18 mm close paren$ ; the second interval is narrower due to lower variability.

Introduction to Confidence Intervals: Videos & Practice Problems