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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.

User Jamk
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6 votes

Answer:

CI (95%)lb = 576,51

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

User Fortisimo
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