Type 1 and type 2 errors
The type 1 error is committed when the true null hypothesis is rejected by the decision-maker or researcher (Black, 2011). For instance, in the event that the process of packaging flour is in control and averages 80 oz. of flour for every package. If this population mean is rejected, then type 1 error is said to have been committed. On the other hand, type 2 error happens when the researcher does not reject a false null hypothesis. If the sample mean gives 80.2 oz. and the researcher decides not to reject the null hypothesis when the population mean is 81 oz. then type 2 error is committed.
Null and alternate hypothesis
The null hypothesis states that the status quo still exists (Black, 2011). If the average of maize flour packages population is 80 oz. The null hypothesis supports it, a process in control. Alternate hypothesis supports the existence of a new theory or state of things. In this same case, the alternate hypothesis will state that the average population is not 80 oz, process out of control.
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Choice of significance levels
Choice of significance level refers to the arbitrary selection of the probability of making type 1 error or simply rejecting a true null hypothesis (Black, 2011). For example, 5% significance level implies that there a chance of this magnitude to make type 1 error.
One- and two-tailed statistical hypotheses for one-sample data
Considering a sample with a mean being compared to a value x at a significance level of 5% using a t-test, the two-tailed hypothesis is that the mean is both significantly greater and less than this figure x (Anderson, Sweeney & Williams, 2011). The one-tailed hypothesis is that the mean of this sample is either significantly greater or less than the value x.
P- Value method
This method entails determining the possible hypothesis by finding the probability of observing a test-statistic that is more of an alternate hypothesis than the one obtained (Black, 2011). It is likely when the p-value is large, over α.
Apply the p-value method
In its use, if the p-value is below or equal to α, the null hypothesis is rejected and the alternate one accepted (Anderson, Sweeney & Williams, 2011). If the p-value is over α, the null hypothesis is accepted. For example, claims about means, proportions, and standard deviations are rejected if the p-value is less than or equal to α.
Hypothesis testing for single populations
Hypothesis testing for single population implies that there is one mean to be evaluated fort a given sample (Anderson, Sweeney & Williams, 2011). In this case, the researcher considers normal distributions of data with just one sample representing the single population.
Statistical inference
Statistical inference refers to the theory, approach, and method used to form conclusions about the parameters of a population as well as the reliability of relationships in statistics on the premise of random sampling (Pelosi & Sandifer, 2003). Therefore, statistical inference is about the researcher making his or her subjective sense of the results got from analysis of data statistically. The inferences made must be logical, despite the random sampling.
Claims made by businesses
Businesses d make claims about different issues related to commerce, finance, and the economy. However, the claims made by businesses can only be proved and validated by research based on the statistical analysis of data (Donnelly, 2012). The statistical methods must be applied to the claims so that they can either be rejected or accepted as valid.
Apply the concepts
The statistical concepts to be applied in this case include p-value method (Donnelly, 2012). For example, the p-value method will be used to compare the claim made with an actual mean of arriving at work. If the p-value is less than or equal to α, the claim will be rejected. This claim will be accepted if the p-value is over α.
References
Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2011). Essentials of modern business statistics with Microsoft Excel . Boston: Cengage Learning.
Black, K. (2011). Business statistics: for contemporary decision making . Hoboken, New Jersey: John Wiley & Sons.
Donnelly, R. A. (2012). Business statistics . London: Pearson Higher Ed.
Pelosi, M. K., & Sandifer, T. M. (2003). Elementary statistics: From discovery to decision . Hoboken, New Jersey: John Wiley & Sons.
