Answer: 625.35
Step-by-step explanation:
Given : Sample size : n= 12, which is less than 30 , so we use t-test.
Sample mean : [tex]\overlien{x}=673\text{ hours}[/tex]
Standard deviation : [tex]\sigma=75\text{ hours}[/tex]
Significance level : [tex]1-0.95=0.05[/tex]
Critical value : [tex]t_{(n-1,\alpha/2)}=t_{(11,0.025)}=\pm2.201[/tex]
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm t_{(n-1,\alpha/2)}\dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]=673\pm(2.201)\times\dfrac{75}{\sqrt{12}}\\\\\approx673\pm47.65\\\\=(625.35,\ 720.65)[/tex]
Hence, the lower bound of the 95% confidence interval for the population mean lifetime of all bulbs manufactured by this new process = 625.35
