A shoemaker claims his best product has an average lifespan

A shoemaker claims his best product has an average lifespan of exactly 14 years. A skeptical customer asks for evidence (data) that might be used to evaluate this claim. The customer was provided data collected from a random sample of 45 people who used the product. Using the data, an average product lifespan of 15 years and a standard deviation of 6 years was calculated. Select the 95%, confidence interval for the true mean lifespan of this product.

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)=15
Standard deviation( sd )=6
Sample Size(n)=45
Confidence Interval = [ 15 ± t a/2 ( 6/ Sqrt ( 45) ) ]
= [ 15 - 2.015 * (0.89) , 15 + 2.015 * (0.89) ]
= [ 13.2,16.8 ]