Question

Please answer with proper steps -

Suppose that a random sample of size n is drawn from a population with mean µ = 220 and standard deviation σ = 20.

i. Determine the required sample size such that the standard error of the sample mean is reduced to less than 3. [2 marks]

ii. Determine the required sample size if we want to be 90% confident that the maximum error is 5.

Answer 1

(i)

the standard error of the sample mean is given by:

Substituting values, w get:

So, we get:

= 45 (Round to integer)

So,

Answer is:

45

(ii)

Sample Size (n) is given by:

Given:

= 0.10

From Table, critical values of Z = 1.645

= 20

e = 5

Substituting values, we get:

= 44 (Round to integer)

Answer is:

44