Question

For the data below construct a 95% confidence interval for the population mean.53.4 51.6 48.0 49.8 52.8 51.8 48.8 43.4 48.2 51.8 54.6 53.8 54.6 49.6 47.2

Answer 1

Answer:

The 95% confidence interval is given below:

$\bar{x} \pm t_{\frac{0.05}{2}} \left( \frac{s}{\sqrt{n}} \right)$

Where:

$\bar{x} = 50.63$ is the sample mean

$t_{\frac{0.05}{2} } =2.145$ is the critical value at 0.05 significance level for df = n-1 = 15 - 1 =14

$s=3.1576$ is the sample standard deviation

$\therefore 50.63 \pm 2.145 \left( \frac{3.1576}{\sqrt{15}} \right)$

      $50.63 \pm 1.75$

      $\left(50.63 - 1.75, 50.63+1.75 \right)$

      $\left(48.88,52.38\right)$

Therefore, the 95% confidence interval for the population mean is (48.88, 52.38)