Answer

1. • Stratified Sampling

     The values of Table 1 are actual monthly income data of a population of 12 families, while Table 2 presents the values of samples of the family samples across income strata. The family groupings in Table 1 indicate the population’s income distribution by household, which formulate the elements/groups from which samples are collected using the stratified random sampling presented in Table 2. The groups/families from which the samples are selected and distributed systematically across strata were randomly selected from the sample space of size 12 by sample sizes.

     However, Table 2 does not present the expected number of samples in each subgroup as it does not follow the systematic proportionality (Sharma, 2017). The distribution of samples per subgroup should be 16.67%, 33.33%, and 50% for the subgroups of sizes 2, 4, and 6 respectively. Therefore, the ideal sample sizes should be:

     For n=2, 16.67% × 1485 = 248 samples (higher than the one in Table 2 by 182 samples)

     For n=4, 33.33% × 1485 = 495 samples (Correctly presented)

     For n=6, 50% × 1485 = 743 samples (Lower than the one in Table 2 by 182 samples)

     But the in the unproportioned distribution of sample across subgroups of families presented diverge from the expected one in stratified random sampling. It is notable that the supposed allocation for subgroup n=2 has been allocated the largest subgroup n=6.

      

      

     Monthly Income Mean

     The average monthly incomes of the samples are presented as $650, equivalent to the population mean. It is, however, expected that there should be variation between subgroups as families have varied monthly incomes and they were picked randomly.

     Group Comparison

     The smaller groups seem to have better distribution across strata, as each stratum had sample composition of subgroup of size n=2, while the subgroup of size n=6 had samples concentrated around the middle with the extreme strata seeming outliers within the group.