Construct a 95% confidence interval for the population mean, μ. Assume the population has a normaldistribution. A random sample of 16 lithium batteries has a mean life of 645 hours with a standard deviation of31 hours. Round to the nearest tenth.
A) (628.5, 661.5)
B) (876.2, 981.5)
C) (531.2, 612.9)
D) (321.7, 365.8)

Question

Quizplus · Accepted Answer

To construct a 95% confidence interval for the population mean when the population is normally distributed and the sample size is 16 (n = 16) with a sample mean ($\bar{x}$) of 645 hours and a standard deviation (s) of 31 hours, we use the formula: $\bar{x} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}}$, where $t_{\frac{\alpha}{2}}$ is the t-score for 95% confidence with $n-1 = 15$ degrees of freedom. Using a t-distribution table or calculator, the t-score is approximately 2.131. Plugging in the values: $645 \pm 2.131 \times \frac{31}{\sqrt{16}} = 645 \pm 16.5$, which gives us (628.5, 661.5).

Construct a 95% Confidence Interval for the Population Mean, μ