Question

what are the conditions and assumptions necessary to construct confidence interval on the mean and the variance separately?

Answer 1

(a) Conditions and assumptions necessary to construct confidence interval on the mean:

     (i) The sample is a Simple Random Sample

      (ii) The population is large relative to the sample

           10n < N,

          where N = Population size. n = Sample size

      (iii) The sampling distribution of the sample proportion is approximately normal.

             np 10

               n (1 - p) 10

(b) Conditions and assumptions necessary to construct confidence interval on variance:

     (i) The population should be Normal Distribution. Confidence interval of is basd on the sampling distribution of

If the samples of size n are drawn from a normally distributed population, this quantity has a distribution with n - 1 degrees of freedom. So, the assumption that the sample is drawn from a normally distributed parameter is a must.

     (ii) When n = Sample Size is large (n > 30), s² = Sample Variance can be used to compute the     Sample variance.