Checkpoint: Error and Confidence Solution

A Bright Idea decides to test a sample of 153 light bulbs at a 90% confidence level. The standard deviation remains 120 hours. What is the confidence interval for a sample mean of 7,250 hours when the confidence level is changed? (Round to the nearest hour.)

$\begin{matrix} z = 1.645 & E = z \cdot \frac{s}{\sqrt{n}} \\ s = 120 & E = 1.645 \cdot (\frac{120}{\sqrt{153}}) \\ n = 153 & E = 15.9589 = 16 \end{matrix} 7250 - 16 \leq μ \leq 7250 + 16 7234 \leq μ \leq 7266$

A Bright Idea can be 90% confident that the population mean will be between 7,234 and 7,266 hours.

Note

Q: If the confidence level is changed to 95%, would the confidence interval be larger or smaller? Explain.

A: The confidence interval would be larger because the value of E is increasing.