Homework: Week 6, Chapter 6 - Essay Example

Homework: Week 6, Chapter 6 Statistics is a branch of mathematics that deals with collection, recording, and analysis of data. Its scope includes research and data analysis for “decision-making”. This paper seeks to explore a case study and to reflect the topic “test of hypothesis”. Case Study95 % Confidence IntervalGiven that a reporter considered a random sample of 725 votes from a population of 12,457 and recorded 338 votes in favor of an issue on the ballot, the 95 % confidence interval is the set of proportions in the range of 0.4299-0.5025.

This defines the range of values within which the population proportion is expected to fall for a 95 % confidence interval. The reporter can claim that between 42.99 % and 50.25 % of the population favored the subject issue on the ballot. However, he must explain that the claim is made at a 95 % confidence level. On the other hand, the researcher cannot offer a definite number to express the population proportion that is expected to favor the issue. This is because there is an expected variation in responses between the selected sample and the general population (Triola, 2011).

Questions Before Printing the StoryAs newspaper editor, I would ask the reporter the following questions to ascertain reliability and validity of the findings. Can you validate the source of your data? Was there any biasness in your sample selection? Did you obtain consent over the data?Reflection: Test of HypothesisTest of hypothesis is one of the topics discussed in the course. It defined steps that should be undertaken in a sequence, so that a decision over a phenomenon could be made. The first step is the formulation of the set of hypotheses to be tested.

This involves both numerical and statement expression of an opinion as a null hypothesis and a contradictory statement as an alternative hypothesis. The null hypothesis and the alternative hypothesis must, however, be mutually exclusive with an identifiable boundary for ‘decision-making’. Once the set of hypotheses is stipulated, applicable test statistics and level of significance are determined and used to set critical value. A computed value, based on the statistic and the set of data for analysis, is then computed for comparison with the critical values.

A computed value that falls within the acceptance range means that the null hypothesis is not rejected, while a computed value that falls outside the acceptance region implies rejection of the null hypothesis. A conclusion is then made with respect to the formulated statements of hypothesis (Triola, 2011).Though the procedure of testing a hypothesis is well defined, there are a number of challenges in its application. Determination of applicable test is one of the challenges faced, because it requires knowledge of many distributions for identification.

Determination of critical values also poses challenges due to the difficulty in reading of distribution tables. Another major challenge in testing the hypothesis is the fact that a mistake at one stage is transferred to subsequent stages. Application of statistical software, however, solves these problems. Test of hypothesis is applicable in industrial decision making such as monitoring processes (Triola, 2011). ReferenceTriola, M. (2011). Elementary Statistics Using the TI-83/84 Plus Calculator.

New York, NY: Addison-Wesley, Pearson Education