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The main objective of the research is to establish whether there are more people living in urban areas than in rural areas. Hypothesized claims will be supported by calculations so as arrive at the correct conclusion. The null hypothesis is accepted when the calculated z- value is less than the z-tabulated value. However, when the calculated z-value is more than the tabulated z-value, the null hypothesis is rejected, thus adopting the alternative hypothesis.
Null hypothesis (Ho): Many people do not live in urban areas
Alternative hypothesis (H1): Many people live in urban areas
Calculated Test statistic for the Proportion
This can be done using the following formula.
Z = (p-hat – p) / sqrt (pq/n)
Where: n = total sample size of both urban and rural population
P - hat = urban population divided by total sample size
P = urban population sample
q = rural sample size
Therefore, n = (52,318 + 37,800) = 90,118
P = 52,318
q = 37,800
P –hat = 52,318/90,118= 0.581
Proportion on q = 37,800/90,118 = 0.419
Proportion of p = 1 – 0. 419 = 0.581
Pq/n = 0.581*0.419/90,118 = 2.70
Square root of pq/n = sqrt 2.70 = 0.00165
P-hat - p = 0.575 – 0.581 = - 0.005
Hence, z = -0.005/0.00165 = -3.03 (ignore the negative sign)
Therefore, the calculated Z = 3.03
Hypothesis validation is done by comparing the calculated z-value with the tabulated z-value, and since the tabulated z-value is not given, there is need to calculate it.
Tabulated z-value calculated
Significance level = 0.01
Assuming a two-tailed test
Therefore, alpha = 0.01/2 = 0.005
Using the normal distribution curve, the tabulated Z-value (0.5– 0.005)
Z (0.495) = 2.575
In this case the calculated z-value (3.03) is more than the z-tabulated value (2.575), thus the null hypothesis should be rejected, thus leading to the acceptance of the alternative hypothesis that states that many people live in urban areas.
Voluntary response sample would best describe the sample. The voluntary response sample, involves people who choose for themselves issues to respond to, especially the general appeal. In fact, voluntary response samples allow people to voluntarily voice their opinions. In this case, the respondents were asked about where they lived, that is, either urban or rural, and everyone had a choice to respond to the question.
Focusing on the sampling method employed in this analysis, the hypothesis test used might not appear to be valid due to the voluntary response sample bias. The sampling method is regarded as bias because people who have strong opinions might negatively influence the response, especially those people with negative opinions.
The choice of sampling method is the most important aspect on any survey research. Even if the study has been properly done, if the sampling method is poor, then the results from the survey cannot be taken as correct. However, large sample size is essentially good for studying a larger population since it is more representative in nature than a small sample size, but it cannot compensate for a poor sampling method. In addition, very large sample size has some limitations in the sense that it is difficult to know the respondents’ representative about the population under study. In fact, a poor sampling method with extremely large sample size does not enable the researcher to know the characteristic of the population studied.
It can be concluded that many people live in urban areas, contrary to the usual expectation that the number of people living in rural areas should be more than the urban dwellers. Besides, it can be ascertained from the calculated results that the null hypothesis is wrong and it should be rejected, thus adopting the alternative hypothesis, which state that many people live in urban areas. Therefore, based on the sample results, it can be concluded that more people live in urban areas than in rural areas.