Question

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 673 hours with a sample standard deviation of 75 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.

Answer 1

Answer: 625.35

Explanation:

Given : Sample size : n= 12, which is less than 30 , so we use t-test.

Sample mean :
`\overlien{x}=673\text{ hours}`

Standard deviation :
`\sigma=75\text{ hours}`

Significance level :
`1-0.95=0.05`

Critical value :
`t_((n-1,\alpha/2))=t_((11,0.025))=\pm2.201`

The confidence interval for population mean is given by :-

`\overline{x}\pm t_((n-1,\alpha/2))(\sigma)/(√(n))`

`=673\pm(2.201)*(75)/(√(12))\\\\\approx673\pm47.65\\\\=(625.35,\ 720.65)`

Hence, the lower bound of the 95% confidence interval for the population mean lifetime of all bulbs manufactured by this new process = 625.35