Inferential Statistics - Term Paper Example

(a) It is important that researchers take into consideration the full range of possibilities whenever collecting data. Moreover, there is a need to systematize these methods according to their predetermined nature, the utilization of open-ended vis-à-vis close-ended questions, and the use of either non-numerical or numerical analysis of data. Researchers gather their data either on a behavioral checklist, test or instrumentation. On the other hand, it could also entail making visits to a research site wherein observations of participants may be conducted without the need for pre-determined questions; or, it could also be an interview of a participant who is allowed to freely express himself or herself on a wide range of topics sans specific questions.

A researcher selects a research method according to whether the objective is to identify a certain type of information that is gathered before the onset of the study, or whether participants will be the source of that information. In addition to this, data may also be in the form of numerical information that is collected using scales of instruments documenting and reporting the participants’ voices. Sometimes, both quantitative and qualitative information are gathered. Instrument data could be reinforced by responses to open-ended questions, or census data may be supported by exploratory yet in-depth interviews.

In carrying out research, I will begin by indentifying the questionnaire that will be administered during the interview. After the questionnaire has been prepared, the sample population will be selected. A series of interviews will be conducted. Each participant in the research will be given a questionnaire to fill. The research questioner will be structured in a manner that does not offend the participant of the research.Only the qualitative design is appropriate for this, particularly with the use of Grounded Theory, because this phenomenon has not been much explored.

The quantitative method will not be effective for this because of the possibility that significant and relevant phenomena may be overlooked because of the focus on theory and hypothesis testing. Moreover, the knowledge generated from the quantitative method could be too abstract to be applicable to the target population. Meanwhile, the mixed methods will not be effective also since this will be too challenging for a single researcher. b) Unbiased estimator is when the parameters used in estimation have a mean equal to the true mean.

Unbiased statistic will sometimes fall above the true value of the parameter and sometimes below. If we take many samples, (Bluman 327). Because its sampling distribution is centered at the true value, however there is no systematic tendency to overestimate or underestimate the parameter. This makes the idea of lack of bias in the sense of “no favoritism” more precise (Moore 238). The properties of a good estimator are:The estimator should be an unbiased estimator. That is, the expected value or the mean of the estimates obtained from samples of a given size is equal to the parameter being estimated.

The estimator should be consistent. For a consistent estimator, as sample size increases, the value of the estimator approaches the value of the parameter estimated.The estimator should be a relatively efficient estimator. That is, of all the statistics that can be used to estimate a parameter, the relatively efficient estimator has the smallest variance. C. The confidence level states the probability that the method will give a correct answer. Suppose we use 95% confidence intervals often, in the long- run 95% of your intervals will contain the true parameter value (Aron, Aron an Coup 452).

Assume the average rent of hiring a bike is 60 minutes. A level confidence interval for the mean x of a normal population with known standard deviation σ, based on an SRS of size n, is given by xz(x= 60 minutesSignificance level 5%, n = 100 and z=1.961.96(1.96(3)54.12≤x≥65.88The mean of the sample should range from 54.12 minutes to 65.88 minutes.D We begin by setting the hypothesis, Ho: μ ≤ 60 minutes (the average length of the bike higher, is the same as 60 minutes). H1: μ >60 minutes (claim) The critical value at α=0.

05 and the test is a right –tailed test is z = +1.96.Calculation of the test valueZ= = =1.667The test value, +1.667, is less than the critical value, +1.96, and is within in the critical region, the decision is accept the null hypothesis.There is enough evidence to support the assertion that the average length of the bike hire is consistent with Transport for London expectation that bikes should be hired for no longer than 60 minutes.Works CitedAron, Arthur, Elaine, Aron & Elliot, Coups.

Statistics for psychology. Pearson: Pearson Prentice Hall, 2006. Print.Bluman, Allan. Elementary statistics: A Step-By-Step Approach. Boston: McGraw Hill Higher Education, 2004. PrintMoore, David. The Basic Practice of Statistics. New York: W. H.Freeman and Company, 2003. Print