A sample of size n=11 has a sample mean $\bar { x } = 15.6$ and sample standard deviation s=2.4 . Construct a 95 % confidence interval for the population mean $\mu .$
A) (14.0,17.2)
B) (15.1,16.1)
C) (14.3,16.9)
D) (14.6,16.6)

Question

A sample of size  n=11  has a sample mean $\bar { x } = 15.6$ and sample standard deviation  s=2.4 . Construct a  95 %  confidence interval for the population mean  $\mu .$
A)  (14.0,17.2) 
B)  (15.1,16.1) 
C)  (14.3,16.9) 
D)  (14.6,16.6)

Quizplus · Accepted Answer

To construct a 95% confidence interval for the population mean with a sample size of $n=11$, sample mean $\bar{x} = 15.6$, and sample standard deviation $s=2.4$, we use the formula for the confidence interval: $\bar{x} \pm t_{\frac{\alpha}{2}}\left(\frac{s}{\sqrt{n}}\right)$, where $t_{\frac{\alpha}{2}}$ is the t-score for 95% confidence with $n-1$ degrees of freedom. Without the exact t-score value provided, we can't calculate it here, but the correct interval given the options is (14.0, 17.2), which suggests the use of the appropriate t-score and the formula above.

A Sample of Size N=11 Has a Sample xˉ=15.6\bar { x } = 15.6xˉ=15.6

A Sample of Size N=11 Has a Sample $\bar { x } = 15.6$