Use the Confidence Level and Sample Data to Find a Confidence

question 87

Multiple Choice

Use the confidence level and sample data to find a confidence interval for estimating the population µ. Round your answer to the same number of decimal places as the sample mean.
-A random sample of 108 light bulbs had a mean life of $\bar { x } = 547$ hours with a standard deviation of $\sigma = 36$ hours. Construct a $90 \%$ confidence interval for the mean life, $\mu$ , of all light bulbs of this type.

• A) \(541 \mathrm { hr } < \mu < 553 \mathrm { hr }\)
• B) \(538 \mathrm { hr } < \mu < 556 \mathrm { hr }\)
• C) \(539 \mathrm { hr } < \mu < 555 \mathrm { hr }\)
• D) \(540 \mathrm { hr } < \mu < 554 \mathrm { hr }\)

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Definitions:

Authoritarian

A dictatorial approach focused on high demands and low responsiveness, often enforcing strict rules and expecting complete obedience.

Indulgent

Exhibiting leniency or a tendency to be overly generous in granting freedom or wishes to oneself or others.

Cultural Goal

Objectives, ideals, or outcomes that are valued and pursued by a community or society, shaping behaviors and norms.

Survival Goal

An objective or aim focused on ensuring the continued existence, safety, and well-being of an individual or group in challenging circumstances.