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a company has developed a new type of light bulb, and wants to estimate its mean lifetime. a simple random sample of 12 bulbs had a sample mean lifetime of 614 hours with a sample standard deviation of 59 hours. it is reasonable to believe that the population is approximately normal. find the lower bound of the 95% confidence interval for the population mean lifetime of all bulbs manufactured by this new process.

Sagot :

Answer:

CI (95%)lb = 576,51

Step-by-step explanation:

Sample Information:

sample size   n  = 12

sample mean  x  =  614 h

sample standard deviation   s  = 59 h

Population with normal distribution, sample size n < 30  in  order to find out CI 95%   significance level is  α = 5 %  α = 0,05   α/2 = 0,025

t(c) for  α/2 = 0,025 and degree of freedom  df =  n - 1   df =  12 - 1  

df = 11  is:

t(c) = 2,201

CI  =  x  ± t(c) * s / √n

CI (95%) =  614  ±  2,201 * 59 / √12

CI (95%)lb = 614  - 37,49

CI (95%)lb = 576,51

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