A hypothesis is a postulation about a situation. The testing ofhypothesis involves evaluating whether the associations between twovariables can be attributed to chance (probability) or not (Brooks,2014). For example, an increase in the price of a car will lead to adecrease in demand. It could also be the case, a rise in the pricesresults in the fall in demand. Notably, the consumers may interpretthe increase to mean better quality and performance. Therefore, ahypothesis has two outcomes, a positive one, where the postulationswere correct or null meaning the guesses were wrong. The only way totest the hypothesis is to gather data on the test subject. The paperwill discuss type 1 and II errors. Furthermore, it will exploreregions of rejecting or accepting a hypothesis.
Question#1:Type I and II Errors
It is possiblethat the conclusion drawn from the statistical analysis is erroneous.Notably, a determination made from the evaluation of the p-value(probability) of an event (hypothesis) occurring. The errors aregrouped into type I and II. In the type I error, a positivehypothesis is accepted, and the null is rejected based on wronginterpretation of observations (Brooks, 2014). For example, if thep-value is 0.01, meaning there is only a 1 chance in 100 tries thatthe null hypothesis will occur. Type II error occur when thepositive alternative is rejected and the null accepted. In this case,the p-value is too big, such that the chances of the unlikely eventoccurring are increased. If the results lie outside the p-value, theycan only happen by random chance and are therefore statisticallyinsignificant (highly unlikely). For example, going back to theexample of the increase in the car price, supposing at significancelevel (α=5%), where the chances of getting the outcome of nullhypothesis are low, an increase in demand is noted. The nullhypothesis will be accepted and Ha rejected. As shown inthe example, type II error puts the consumer at risk of buying acheap product more. Notably, the p-value denotes the probability ofhaving a result that is equal or extreme than what was observed.
Question#2 Rejection and Non-Rejection Regions
The twostatistical methods applied in making a decision regarding the nullhypothesis (Ho) are the p-value and rejection andnon-rejection regions. The former is the most widely used. Nullhypothesis means no difference between the compared variables. Thechart below gives a simplified way of understanding the regions. Theµ0 defines the population mean, the αs denote criticalvalues that indicate the boundaries of the rejection andnon-rejection areas. Notably, the smaller the α, the slimmer thechance of the null hypothesis occurring and the more confidence inthe obtained data (Brooks, 2014). The approach to developing therejection and non-rejection regions is to use z-test or t-test todevelop the critical values (αs). Areas that are extreme or equal tothe critical values are called rejection regions. In other words, thevariable is highly unlikely to occur. On the other hand, the unshadedarea is called non-rejection region. Suppose in the study, 500consumers were interviewed, and 278 of them said they would buy thecar. It can be concluded more than 50% are willing to purchase thevehicle at 5% significance level. The two hypothesis are H0 p=50% and Ha p>50%.
In conclusion,the t-test chart above at 5% significance level shows the Ha iswrong. The truth is the demand for the car will not drop with anincrease in price. Notably, the rejection and non-rejection methodsachieve the same objective as the p-value. They determine whether anull hypothesis is correct or not. Type I errors leads researchers toreject the null hypothesis and type II to its non-rejection.
Brooks, C.(2014). Introductory econometrics for finance. Cambridgeuniversity press.
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