Various Aspects of Statistics Particularly those Involving Sample Side Determination (Coursework Sample)

More Advanced Statistical Measures
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Mean and Standard deviation
Mean and standard deviation can provide a vital facts regarding the debt level of the sample. The data on the debt levels of 100 elements were entered in the SPSS and analyzed. The output results obtained by running the data via SPSS, reveals that the sample has a mean debt and standard deviation of $ 96197.53 and $ 3487.78 respectively.
Making Inference
Statistical inference has been of great use among researcher owing to the fact that it is not practically possible to study the characteristics of the entire population. By definition, statistical inference entails deducting characteristics of an underlying distribution by primarily analyzing a given data set (Zacks, 2014). We can confidently infer that the sample mean is the mean debt in the population mainly for two reasons. First, the sample size of 100 is large (n>30). This implies that the sample is arguably an accurate mean estimate of the population parameter. Moreover, the data sample is normally distributed, which means that the p-values and confidence intervals are valid used are valid.
Confidence interval computation (95%)
Confidence interval forms an important part of statistical analysis since provides a wide range of values that are likely to have the population parameter of interest. That is, it provides the probability that the interval provided by the employed method consists of the true value of the population parameter. Confidence intervals mostly used ranges from 90% to 100%, with 95% and 99% as most used intervals (Feingold, 2015). With the mean of $ 96197.53 and standard deviation of $ 3487.78, the confidence interval of 95% will be:
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=$ 95513.9 to $ 96881.1
Interpretation of the results
The results from the above computation of the confidence interval of 95% reveal that there is a 95% chance that the population’s mean debt falls between the debt of $ 95513.9 and $ 96881.1. This chance can be improved if we increase our confidence level from 95% to 99% of more.
Sample size determination
The size of the sample significantly determines the precision of the results. Given a particular level of confidence and width (desired accuracy), it is possible to determine the sample size. If the accuracy of the sample mean is to be within a range of -/+$1,000 from the true population mean, the size of the sample will be determined as follows.










From the above computation, the researcher will require a sample of approximately 47 households.
Steps to ensure than the sample is representative
As noted earlier, it is impractical to correct data from every element in a population. For this reason, we largely depend on the representativeness of the sample we adopt to make generalization regarding the target population. To be considered representative, the characteristics of the sample selected should closely match those found in the target population. In an effort geared towards increasing the representativeness of the sample, careful considerations should be made on a number of issues. First, there is need to adopt probability sampling techniques as op...