Question

Osmar Ltd conducted a study to determine the lifetimes of the light bulbs produced by their Melbourne plant. Based on studies in other plants, it could be assumed that the variance of the lifetimes was 100000 hours squared. Experimental testing of 50 light bulbs yielded an average lifetime of 27.7 hundred hours. Construct a 90% confidence interval for the average lifetime of the bulbs produced in Osmar's Melbourne plant. Report the lower limit in hours to 1 decimal place.

Answer 1

Average lifetime = 27.7 hundred hours = 2770 hours

Variance = 100000

Standar Deviation = sqrt(100000) = 316.2277 Hours

standard error of sample mean = 316.2277/sqrt(50)= 44.72 hours

90% confidence interval for the average lifetime of the bulbs produced in Osmar's Melbourne plan

= Ssample Mean +- Margin of error

Margin of error = Critical test statistic * standard errorf samplemean

= 1.645 * 44.72 = 73.56666

90% confidence interval = 2770 +- 73.5666 = (2696.4 hours 2843.57 hours)