Question

The life in hours of a certain type of lightbulb is normally distributed with a known standard deviation of 10 hours. A random sample of 15 lightbulbs has a sample mean life of 1000 hours. What would the 99% lower-confidence bound L on the mean life be, rounded to the nearest integer?

Answer 1

Solution :

Given that,

= 1000

s = 10

n = 15

Degrees of freedom = df = n - 1 = V - 1 = 14

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t _/2,df = t_0.005,14 = 2.977

Margin of error = E = t_/2,df * (s /n)

= 2.977 * (10 / 15)

= 7.686

Margin of error = 7.686

The 99% confidence interval estimate of the population mean is,

- E < < + E

1000 - 7.686 < < 1000 + 7.686

992.314 < < 1007.686

(992.314, 1007.686 )