In: Math

# what are the conditions and assumptions necessary to construct confidence interval on the mean and the...

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

## Solutions

##### Expert Solution

(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.

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