Respuesta :
Given Information:
Number of lithium batteries = n = 16
Mean life of lithium batteries = μ = 645 hours
Standard deviation of lithium batteries = σ = 31 hours
Confidence level = 95%
Required Information:
Confidence Interval = ?
Answer:
[tex]CI = 628.5 \: to \: 661.5 \: hours[/tex]
Step-by-step explanation:
The confidence interval is given by
[tex]CI = \mu \pm t_{\alpha/2} (\frac{\sigma}{\sqrt{n}})[/tex]
Where μ is the mean life of lithium batteries, σ is the standard deviation, n is number of lithium batteries selected, and t is the critical value from the t-table with significance level of
tα/2 = (1 - 0.95) = 0.05/2 = 0.025
and the degree of freedom is
DoF = n - 1 = 16 - 1 = 15
The critical value (tα/2) at 15 DoF is equal to 2.131 (from the t-table)
[tex]CI = 645 \pm 2.131(\frac{31}{\sqrt{16}})[/tex]
[tex]CI = 645 \pm 2.131(7.75})[/tex]
[tex]CI = 645 \pm 16.515[/tex]
[tex]CI = 645 - 16.515 \: and \: 645 + 16.515[/tex]
[tex]CI = 628.5 \: to \: 661.5 \: hours[/tex]
Therefore, the 95% confidence interval is 628.5 to 661.5 hours
What does it mean?
It means that we are 95% confident that the mean life of 16 lithium batteries is within the interval of (628.5 to 661.5 hours)
