the lonco Electric company advertising that their new 90 wat

the lonco Electric company advertising that their new 90 watt Extend life light bulbs have an average lifetime of 2500 hours . The consumer protection Agency tested a sample of 150 lonco 90 watt extended life bulbs and computed the mean and standard deviation as 2460 and 201 hours respectively . Comput a 95% confidence interval for the average lifetime of all Lonco extended life 90 watt light bulbs , and then say if the consumer protection Agency found the Lonco Electric Company in or out of compliance with the Fair Advertising Act.

Solution

CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=2460
Standard deviation( sd )=201
Sample Size(n)=150
Confidence Interval = [ 2460 ± t a/2 ( 201/ Sqrt ( 150) ) ]
= [ 2460 - 1.976 * (16.412) , 2460 + 1.976 * (16.412) ]
= [ 2427.571, 2492.429 ]