Question

Construct the discrete series. Count unbiased estimates of the general mean and general variance. Find the confidence interval for expectation with a confidence level of 0.05 5, 11, 13, 9, 11, 5, 7, 7, 5, 9, 13, 13, 11, 9, 5, 9, 11, 9, 5, 9, 11, 9, 9, 5

Answer 1

Data set: (5, 11, 13, 9, 11, 5, 7, 7, 5, 9, 13, 13, 11, 9, 5, 9, 11, 9, 5, 9, 11, 9, 9, 5)

$Mean=\frac{\Sigma X}{n}=\frac{5+11+13+9+11+5+7+7+5+9+13+13+11+9+5+9+11+9+5+9+11+9+9+5}{24}=8.75$

Following table shows the calculation of standard deviation:

$s=\sqrt{\frac{\Sigma(X-\bar{X})^2}{n-1}}=\sqrt{\frac{170.50}{24-1}}=2.72$

Formula for the 95% confidence interval is:

$CI=\bar{X}\pm Z\frac{s}{\sqrt{n}}$

$CI=8.75\pm 1.96\times\frac{2.72}{\sqrt{24}}$

$CI=8.75\pm 1.09$

$CI=(7.66, 9.84)$