Statistics questions (Essay Sample)

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There are two forms of hypothesis in statistics, null and alternative hypotheses. Null hypothesis, H0 is an explanation regarding a statistical phenomenon from a set of data that is assumed to be valid unless actual analysis turns to contradict the said phenomena behavior. However, an alternative hypothesis, H1 which is otherwise called the research hypothesis is one which specifies that the said null hypothesis does not hold. Statistical analysis has to be carried out in the alternative hypothesis to prove if null hypothesis is true.
Statistical hypothesis testing is a form of decision making from a given data set. It carries with it one or two sample tests from a controlled experiment. One sample test is carried out when the characteristics of a sample are being compared to a population which has a given hypothesis. The attributes of the population are known with certainty. On the other hand, two sample tests are carried out on in order to compare attributes from two different samples which arise from identical controlled experiments.
Flaws are made when making tests on the null hypothesis. Whereas type 1 error specifies the case where a hypothesis is rejected when it should have been accepted, type 2 error is a kind of error made when a hypothesis is accepted when it ought to have been rejected. In other terms, type 1 entails rejection of a true hypothesis but type 2 is the acceptance of a false hypothesis. If proper procedures are followed during the tests then type I of error is controllable.
Paired and unpaired samples are the two forms of samples that can be applied in two sample tests. Paired samples are also known as dependent samples as they contain pairs of units that are matched together. The matched pairs are similar in character or are in groups that have been tested twice in a controlled experiment. Unpaired samples are independent in nature as they have been formed from two populations being compared.
Regression has been applied in several fields of business to forecast various variables. One notable area of application is in the production level of business. Here, the cost of producing one unit of a given product is outlined as a function of several factors including costs of labor, electricity, raw materials, transport and so on. The variability of those factors determines the outcome of the cost the output in terms of their magnitude. The other use is on estimating the growth level of the country’s gross domestic product, GDP. The determinants of GDP are studied and their relationship determined by the various government agencies to help come up with policies that will positively contribute to its growth. Lastly profitability of the firm can be influenced through placing the trading and profit account major components in the regression model to ascertain their relationship with the net profits.
The two forms of regression in statistics are the simple linear regression and the multiple linear regressions. Simple linear regression is the less complex one. It brings out the relationship of only one independent variable and the dependent variable in the form of Y=a + b X. where y variable is plotted on the y-axis and x variable on the x-axis. In addition, from the graph we can deduce that b is the slope f the resultant curve but “a” becomes the y-intercept...