Assignment on Sampling and G Power Analysis

Running head: SAMPLING AND G* POWER ANALYSIS 1
Sampling and G* Power Analysis
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SAMPLING AND G* POWER ANALYSIS 2
Sampling and G* Power Analysis
Question 1 (A)
The study below will illustrate the steps that should be taken when critically analyzing a
stratified sample of 75 lawyers, 75 engineers and 75 doctors who belong to a single professional
entity. The most likely occurrence of such a statistic sampling analysis could be within the
banking system when the accountant is keying in the gross income of their banking members
(pension owners, insurance covers, stakeholders, shareholders and C.M.O or C.D.O) to gauge the
profitability of their clientele’s income and interest rates. In any estimation analysis, the main
objective is obtaining an estimator of the population sample that can assist in taking care of the
salient or essential features that would help in describing the population. The method of simple
random sampling will offer homogeneous samples. Thus the sample mean serves as a proper
estimator of a sampled population mean especially if the community was homogeneous
concerning the trait put under study. Consequently, the sample that is drawn through simple
random sampling is needed to offer a representative sample variable if the population under
study is homogeneous to the trait being investigated.
As shall also be observed, the sample mean relies upon the population variance as much
as it also relies upon the sampling fraction and size. The study has to use a sample scheme which
minimizes the heterogeneity within the population, thereby increasing the estimator's precision.
Suppose the population is heterogeneous to the trait under study, then the sampling process to be
applied is deemed as stratified sampling (Mumby, 2002, pg.85-87). Ideologically, stratified
sampling entails dividing the whole heterogeneous population into smaller sub-sections or sub-
populations in which the sampling units should be homogeneous to the trait under study within
each sub-section or sub-population and heterogeneous among the sub-sections to the character

SAMPLING AND G* POWER ANALYSIS 3
under investigation. Thereby, these subpopulations are usually termed as strata. In this case, the
sub-sections are doctors, lawyers and engineers and the characteristic under study are their
interest rates and income. Each subpopulation is treated as separate variables, and SRS draws a
sample from every stratum.
Moreover, in such a study, the population can be divided into stratum 1 (doctors), stratum
2 (lawyers) and stratum 3 (engineers). All the illustrated samples above assist in constituting to
the final stratified sample for further researches. Furthermore, the following notations and
examples are used in analyzing a stratified sample: Population size (N), number of strata (K),
and sampling unit numbers in i, (Ni).
The procedure that should be followed when analyzing the stratified sample above begins
with dividing the whole population N into k strata. We let the ith stratum which contains
Ni,i=1,2...,k unit numbers. In this case, N=75 and k=3 since we have three layers. The strata
should not overlap and homogeneous to the trait under study as indicated with summation from
i=1 to k on Ni=N. The sample size ni is drawn from ith (i=1, 2,...k) using either SRS or preferably
WOR in each stratum independently (Passmore & Baker, 2005, pg. 45-56). Thereby, a stratified
sample size n=summation from i=1 to k of ni shall be constituted in which case the values to each
stratum’s income or interest rates shall be generated if used as the characteristic under study.
Other estimators can further be used to evaluate the stratified sample, and these include the
mean, variance and standard deviations which could still pave the way for conducting regression
and correlation analyses.
Question 1 (B)

SAMPLING AND G* POWER ANALYSIS 4
Suppose the sample population being investigated comes from a simple random sample
then a proper analysis should offer the following two outputs namely; point estimate of the
proportion or sample population mean and a quantitative assessment of uncertainty associated
with point estimates such as confidence intervals, margins or errors (type I or type II errors). In
this second scenario, the question needs a simple random sample analysis of 150 subscribers to
the local newspaper. The investigation being conducted is simple random sample, and thus some
of the characteristics that can be put under study entail the number of consumers who prefer a
particular news media newspaper, name of newspaper sold during the day, the interest rates
generated after 150 subscribers have purchased the paper and the number of consumers who buy
the paper at different times of the day. The sampling method has two variables (one changing
equally and spontaneously and the other constant) and constant co-efficient (Robertson, Andrew,
and Chris, 2018, pg. 27-48).
The steps that should be followed when analyzing a simple random sample should
include the following steps: estimating population parameter, estimating population variance,
computing standard errors, specifying confidence levels, finding the critical values often the t-
test and z-test, computing error margins and finally defining the confidence intervals. The first
step as earlier stated was estimating the population mean in this case; we could have estimated
the sample mean as the income generated throughout the day sales (observations with attribute)
divided by the 150 (total sample size), which is the number of total subscribers. The second step
entails finding the population variance which is calculated as s2 = Σ (xi - x )2 / (n - 1) (Owen,
Yury Maximov, & Michael, 2019 pg. 231-254). After the above calculation, the standard errors
are computed SE = sqrt [ (1 - n/N) * s2 / n], which is also known as the standard deviation of the
sample statistic being computed. The following step entails the specification of the confidence