1i) In a survey of households, a simple random sampling without replacement was used to select sample of size 50 from a

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1i) In a survey of households, a simple random sampling without
replacement was used to select sample of size 50 from a village
consisting of 625 household. The aim was to estimate the mean
household expenditure on Kitchen tools The estimate was found to be
GHS 42.00 with a Standard error of GHS 4.70. Using this information
determine the sample size needed to estimate the same
characteristic in a neighbouring village on the basis of a sample
selected with Simple Random sampling with replacement such that the
length of the confident interval at 95% level is 20% Of the true
value. State the assumption involved in finding the sample
size.
ii)In a sample of 200 Graduates selected from a population of
2,000 Graduates with SRS without replacement. 140 Graduates were in
favour of a new Tax regime.
a) Estimate the 95% confidence limit for the number of Graduates
in the population in favour of the proposal.
b) Do the above data furnish sufficiently evidence at 95%
confidence level to reject the hypothesis that only 50%of the
Graduates are in favour of the proposal?
c) What sample size would reduce the expected length of the 95%
confidence interval to half its length in (𝑎)?
iii)Given the ratio estimator 𝑹̂ = 𝒚̅⁄𝒙̅ ; derive the sample
variance the ratio estimator 𝑽𝒂𝒓( 𝑹̂) .