Question

a) In order to estimate the population mean, μ, to within 3 at 95% confidence, what is the minimum sample size required? (Assumeσ=6.7).

b) If just the population standard deviation were to increase, then the minimum sample size required would:

decrease /increase   

c)  If just the confidence level were to decrease (i.e. go from 95% to 90% confidence), then the minimum sample size required would:

decrease/increase   

d) If just the bound within which μ was to be estimated were to increase, then the minimum sample size required would:  

decrease/increase

Answer 1

Solution :

(a)  

Given that,

standard deviation = = 6.7

margin of error = E = 3

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 * 6.7 ) / 3)²

= 19.16 = 20

Sample size = 20

(b)

The population standard deviation were to increase, then the minimum sample size increase .

Answer : Increase .

(c)

The confidence level were to decrease (i.e. go from 95% to 90% confidence),

then the minimum sample size required would decrease .

Answer = Decrease .

(d)

The bound within which μ was to be estimated were to increase, then

the minimum sample size required would increase .