| Category | Assignment | Subject | Business |
|---|---|---|---|
| University | Singapore University of Social Sciences | Module Title | Statistics (BUS105) |
Under BUS105, you will be given a general idea of what statistics techniques and concepts are, so that you could be able to obtain information that is applied in making a decision. Different topics are discussed in the course, which encompass probability, distributions, interval estimation, ANOVA, hypothesis testing and regression. Learning interpretative and analytical skills, which will be required in the understanding of the statistical findings, will be the main focus.
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Statistical data is merely the aggregation of numbers that are employed to demonstrate a part of the information representing a large number of people. As an example, you may want to survey a population of 1000 people, then you will not have to send a survey to every person out of 1000; you will randomly select 200 people, and the data that you will receive is statistical data.
The primary reason why statistical data is needed is to assist in the decision-making process by giving valuable insights as to what the data would say about the larger population.
Statistical information may be represented in a tabular or graphic form, and various forms of charts and graphs are employed in presenting the data in different facets of data. Box plots, frequency polygons and histograms are some of the common types of graphs that are used to represent statistical data.
Probability: Probability is merely a measure of the likelihood of happening of an occurrence happening. Probability may be expressed either in percentage or in a decimal, whereby 0 indicates no possibility of that event and 1 indicates complete possibility that that event will happen.
Mean: It is the mean of the data given. To compute the mean, all one has to do is simply sum up all the values that are in the set, and then divide them by the total values in that set. To illustrate, you have to find out the average age of 10 individuals. You add all the ages of the 10 individuals, and then the total number is divided by 10.
Standard deviation: It summarises the distribution of the values in a numerical collection. The variance’s square root is simply taken to calculate a standard deviation. The average of the squared differences between the means obtained is taken to get the variance.
Sample mean and proportion are two significant statistics which are employed to depict a population in statistics. The mean of a sample is the arithmetic mean of a sample, whereas the proportion is the percentage of individuals in a sample that belong to a specific category. These two measures can be utilised in estimating the population statistics; however, it is necessary to know how they are determined, as well as their limitations.
With the mean, a 95% confidence interval implies that given that we are going to repeat our study many times, 95 per cent of the time the population means would be between our calculated interval.
In the proportion, the 95% confidence interval indicates that given that we were to rerun our study repeatedly, 95 per cent of the time the true population proportion would lie within the interval that we have calculated.
A hypothesis test is of two different categories: the one-sample and the two-sample.
When you desire to compare a sample mean to a population mean, then it is a one-sample test. Two-sample test is applied when you want to compare the means of two items or people, as in the case of the means of two groups.
In these two tests, the first is the null hypothesis, which means there is no difference between the population mean and sample mean (or between the two means of the groups), whereas the other hypothesis means a difference is available.
A one-sample test is normally applied in cases where there is a small sample size (n less than 30). The test of two samples is more commonly applied when the sample size (n) is large (n > 30).
To do a one-sample test, you will have to compute the standard error and the z-score. Standard error: Standard error is basically the standard deviation of the sampling distribution. It is determined as shown by the following formula:
SE = s / [?]n
Where s is the standard deviation in the sample, and n is the size of the sample.
The ANOVA procedure is employed when comparing the means of two or more groups of independent variables. This process will enable establishing the existence of a statistically significant difference between the groups of means. To do this, the ANOVA procedure is used to compare the variability within each group to the variability between the groups.
When the variability in the groups is higher than that in the other groups, then it is considered that any statistical difference is not seen among the means of the groups. There is no statistically significant difference between the means of the groups. On the other hand, when the variation between groups is high as compared to that within groups, it can be considered that there is a statistically significant difference among the means of the groups.
The steps used to conduct the ANOVA procedure are as follows:
The process of fitting a linear regression line to some data follows a few steps. To begin with, you must possess some data points that can be fitted with the line. This information may derive from anything, recent sales data, survey data, etc. After getting your data set, you will then be required to select the variable that will be your dependent variable (that which you are attempting to forecast) and one that will be your independent variable (that which you are utilising to forecast the dependent variable).
Once this is done, it is just a matter of putting the variables in a linear regression equation and solving to get the slope and intercept. When you have those values, you are able to plot the line on a graph and assess the level of fit.
The equation of the linear regression is:
Y = mX + b
Y is the dependent variable, X is the independent variable, m is the slope of the line, and b is the y-intercept.
You can use the following formula for calculating the slope of the line: m = (∑XY – (∑X)(∑Y)) / (∑X2 – (∑X)2)
Where ∑XY equals a sum of the products of each X and Y value, ∑X is the sum of all X values, ∑Y equals a sum of all Y values, and ∑X2 equals a sum of the squares of all X values.
It is possible to determine the y-intercept using the formula below: b = (∑Y – m(∑X)) / n
After getting the slope and y-intercept, you can then insert them in the linear regression equation and predict using them with respect to the dependent variable.
It is possible to explain the results of a multiple regression in several ways. The only major consideration one has to make involves the fact that these results are just quantitative projections; they cannot be used to form any causal conclusions.
The values in the coefficient of the predictor variables are taken to get an interpretation of the findings. A coefficient value of positive nature implies that as the predictor variable increases, the response variable is also expected to increase. Having a negative coefficient will indicate inversely that the response variable should decrease with an increase in the value of the predictor variable. The magnitude of the coefficients can be justified by the fact that it is an indication of the degree to which the particular predictor affects the response variable.
Another way of interpreting the results of the multiple regression analysis is using analysis of variance (ANOVA). This dictates the importance of the whole model and that of the individual variables of prediction. Significant models mean that there is a relationship between the response variables and predictor variables, but a non-significant model simply indicates that there is no such relationship between predictor variables and response variables. To determine the importance of individual predictor variables, it is possible to review the p-value of each of them. The p-value that is not zero and not greater than 0.05 indicates that the variable is significant.
Based on the multiple regression findings, they may be difficult to interpret; hence, you need to seek assistance or guidance from a statistician or any other qualified individual if you are not certain about the next step of action.
Microsoft Excel was the data analysis package that I used to perform the analyses in this course. Excel was a convenient and simple application in my task of working on all the statistical concepts and methods I learned throughout this course.
A result of a given statistical analysis can be highly useful in making a decision. The analysis of past data allows the analysts to give a response and forecasts of what may occur in the future. This is more so in business, as awareness of what may occur can assist the executives in making crucial decisions regarding investments, production level, and marketing strategies.
To illustrate, we will have a company that is about to introduce a new product. They can employ the statistical analysis to forecast the success of the product on the basis of the previous releases of the same product. This information can be utilised further to make production-level choices, prices, and advertising decisions.
The trends of customer behaviour can also be learned through statistical analysis. Through observations of data, the analysts can determine the probability of customers making some decisions, like moving to an alternative product from a competitor. The marketing and sales strategies can be informed by this information.
It is possible to present statistical analysis and findings in oral presentations in the classroom or on tape. In both situations, one should be specific and short and at the same time precise and comprehensive.
Summarising the findings and statistical analysis, it is good to begin with a little bit of an overview of the study or data set. This would consist of the objective of the work or data collection, the population under which the work was carried out, the technique employed and the key findings.
Then, you are to present a certain study or data findings. Make sure to explain how every finding was calculated and what it includes with respect to the general research question. Lastly, you are supposed to give a conclusion on what you consider the most important findings of the study or data set.
There are numerous prerequisite knowledge and social skills that are necessary to be a productive member of a team. To become a good team member, one should possess good communication skills, be able to work with people towards a common aim and have good conflict-solving skills. Knowledge of the specific goals and objectives of the team is also necessary to contribute effectively.
Interpersonal skills like these are necessary for every member of the team to enable the team to operate smoothly and attain its goals.
Statistical report is a significant aspect of a business. Data collection and analysis help businesses to make superior decisions regarding the resources they should deploy and the ways of enhancing their products and services.
Being a business writer, you are expected to be conversant with the art of statistical report writing. This implies the ability to tabulate information properly and in a clear and concise form. It also implies that one should be in a position to comprehend elaborate statistical terms and translate them into a non-expert's understanding.
Most importantly, one should be precise and honest in reporting. Business is dependent on statistical reports to make sound decisions, hence the importance of ensuring that the statistical data used is precise and impartial.
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