Question

# The​ quality-control manager at a compact fluorescent light bulb​ (CFL) factory needs to determine whether the...

The​ quality-control manager at a compact fluorescent light bulb​ (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7540 hours. The population standard deviation is 735 hours. A random sample of 49 light bulbs indicates a sample mean life of 7,288 hours.

Construct a​ 95% confidence interval estimate of the population mean life of the light bulbs?

___ <= MU <= ___ (Round to the nearest whole number as​ needed.)

Solution:

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± Z*σ/sqrt(n)

From given data, we have

Xbar = 7288

σ = 735

n = 49

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

Confidence interval = Xbar ± Z*σ/sqrt(n)

Confidence interval = 7288 ± 1.96*735/sqrt(49)

Confidence interval = 7288 ± 205.7962

Lower limit = 7288 - 205.7962 = 7082.20

Upper limit = 7288 + 205.7962 = 7493.80

Confidence interval = (7082, 7494)

7082 ≤ µ ≤ 7494

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