Question

LightsPlus Ltd conducted a study to determine the lifetimes of the light bulbs produced by their Brisbane plant. Based on studies in many other plants, it could be assumed that the variance of the lifetimes was 90000 hours squared. Experimental testing of 51 light bulbs yielded an average lifetime of 21.9 hundred hours. Construct a 90% confidence interval for the average lifetime of the bulbs produced at the LightsPlus Brisbane plant. Report the lower limit in hours to 1 decimal place.

Answer 1

We are given with following information: Variance = 90000^2

Mean(average lifetime) = 21.900 = 2190 hours

n = 51

z-value for 90% confidence interval = 1.645

Sample mean = 2190

Standard deviation = 90000

Standard error of mean = σ / √ n

Standard error of mean = 90000 / √ 51

SE = 90000/7.141428

Standard error of mean = 12,602.5208

Confidence interval 2190 - (12,602.5208)*(1.645) and 2190 + (12,602.5208)*(1.645)

(-18541.1467, 22921.1467)

upper limit = 22,921.1 hours