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Statistical Inference

Statistical inference is the process of drawing conclusions or generalizations from the data of interest. Contrary to descriptive statistics, the practice of statistical inference aims to extrapolate from the observed data patterns and explain how the population at large is affected. Generally, a sample of the total population is analyzed and through statistical inference, the larger picture is realized.

Statistical inference allows the theoretical world and the real world to become connected. The theoretical world consists of the statistical and scientific models being used; the different distributions the samples are taken from; the measures being estimated; and the conclusions being conceived from a statistical view point. On the other hand, the real world parallels the populations being evaluated, from which the samples originate. Statistical inference is the medium through which these two worlds can unite so that observable phenomena can be explained.   

Often, statistical inference involves the approximation of parameters because the absolute value is unknown. Especially if the distribution being used is in question, an estimation of the unknown distribution is required. In addition to estimating unknown parameters, statistical inference also tries to set confidence or creditable intervals, assume the model type being used, conclude on the hypotheses and classify data points.

Statistical inferences can be extended beyond the information presented in the data set under investigation. However, it is important that researchers are cautious when constructing these types of generalizations, ensuring that they can be justified and thus, not result in false conclusions. This would be problematic considering that the overall objective of statistical inference is to formulate conclusions and understand the true behaviour of different populations. 

Categories within Statistical Inference

Sampling Distribution

Postings: 102

The sampling distribution is a theoretical concept which describes the range of values from which a statistic is likely to be found and the frequency of selecting a particular value.

Factor analysis and its assumptions

What is factor analysis statistical method, its test assumptions, and when is this test appropriate to use? How many independent and dependent variables are generally involved?

Stevens' four scales of measurement

Compare and contrast Stevens' four scales of measurement. Explain when each type of scale should be used, such as the nominal scale, ordinal scale, the interval scale and ratio scale. Please provide sources.

Relationship of T-test and Effect Size

Can you explain the data what are the assumptions of correlated groups t test provided? 1.What are the assumptions of a correlated groups t test? 2.What measure of effect size is used for a correlated-groups t test? 3.The student decides to conduct the same study using a within-participants design in order to control for di

Solving and analyzing hypothesis testing question

Chapter 14 Chapter 14 ( total 10 points = part I and part II) 2. A member of the state legislature has expressed concern about the differences in the mathematics test scores of high school freshmen across the state. She asks her research assistant to conduct a study to investigate what factors could account for the differences.


4. At α = 0.05 and 0.10, test the hypothesis that the proportion of Consumer (CON) industry companies winter quarter profit growth is more than 1percentage point greater than the proportion of Banking (BKG) companies winter quarter profit growth, given that p CON = 0.20, p BKG = 0.14, nCON = 350, nBKG=400. P1 = 0.20, Pbkg

Statistics - Chi-Square and Contingency Tables

12. In a contingency table, when all the expected frequencies equal the observed frequencies the calculated 2 statistic equals 1. FALSE 13. In a contingency table, if all of the expected frequencies equal the observed frequencies, then we can conclude that there is a perfect dependence between rows and columns. TRUE 14.

Understanding a Published Study

Based upon the attached article, please give me ideas to address these questions: 1. What statistical test was used in Nelson et al., (2010)? 2. Did the authors use the correct statistical test? In other words, what was their rationale for using this test (i.e., were the variables discrete or continuous and was the test appr

Inferential Statistic: T Test

1.) A student wants to study the effect of two different nursing care models on quality scores of a several units in a hospital. The possible quality scores that the units can have are from 1 to 5, with 1 being the lowest and 5 the highest. One nursing care model involves a decentralization of tasks to a team of licensed and unl

Inferential Statistics Using T-Test

A student studied the effect of diabetic disease management on patients' A1C blood test results. The student placed 22 new diabetic patients that presented at a local clinic into two groups: 12 were placed in a group in which the patients received the usual treatment plus they additionally received disease management care; 10 we

Decision Making and Calculating Costs for a Warehouse

1) What did the original solver solution show as the minimum cost per month? 2) What will be the minimum cost per month if Indianapolis is shut down? 3) What will be the minimum cost per month if all the warehousing is moved to Louisville? 4) What other factors should enter the decision process, and what information do they n

Scheduling New Workers, Choosing a New Work Schedule

How many of each type of worker should AAD hire? Compare the old schedule that includes overtime on weekends for the regular workers to the new schedule. How much is the company saving? If the company could find only ten qualified part-time workers and six new hires, what would be the configuration and cost? Problem In

Forecasting using Excel

ALOMEGA PHARMACEUTICALS Alomega Pharmaceuticals is a small to mid size pharmaceutical company. The accounting department began extending its historical records by recording the sales volume for each month over the past four years, starting in January. The company engages in various kinds of direct to consumer advertisin

Statistical Inference Problem Set

Please help with the following problems. (i) Let {Xi} be a sequence of rv's that converges in probability to a constant a. Assume that P(Xi > 0) = 1. a) Show that the sequence {Yi} defined by Yi = sqrt(Xi) converges in probability to sqrt(a). b) Show that, if a>0, the sequence {Zi} defined by Zi = a/Xi converges i

Statistics: Type I and Type II Error Analysis

A large courier company sends invoices to customers requesting payment within 30 days. The bill lists an address and customers are expected to use their own envelopes to return their payments. Currently the mean and standard deviation of the amount of time taken to pay bills are 24 days and 6 days, respectively. The chief financ

Statistical inference to business decision scenarios

The manager of the Gander Mountain store in Frogtown, IL, believes that his prices for ammunition are lower than the prices of his primary competitor in the hunting equipment market, Cabela's. He would like to be able to provide evidence to support this assertion. -What are the Gander Mountain manager's null and alternative h

Inference about population mean

Comparing two drugs. Makers of generic drugs must show that the do not differ significantly from the "reference" drugs that they imitate. One aspect in which drugs might differ is their extent of absorption in the blood. Table gives data taken from 20 healthy nonsmoking male subjects for one pair of drugs. This is a matched

Statistics - Inference about a population mean

The placebo effect. The placebo effect is particularly strong in patients with Parkinson's disease. To understand the workings of the placebo effect, scientists measure activity at a key point in the brain when patients receive a placebo that they think is an active drug and also when no treatment is given. The same six patie

Inference about a population mean

Calcium and blood pressure. In a randomized comparative experiment on the effect of calcium in the diet on blood pressure, researchers divided 54 healthy white males at random into two groups. One group received calcium; the other, a placebo. At the beginning of the study, the researchers measured many variables on the subjects.

Simple Statistics Problems - Problem 3-77 Suppose that 5 of a total of 20 company accounts are in error. An auditor selects a random sample of 5 out of the 20 accounts. Let X be the number of accounts in the sample that are in error. Is X binomial? If not, what distribution ... [See the Attached Questions File.]

Problem 3-77 Suppose that 5 of a total of 20 company accounts are in error. An auditor selects a random sample of 5 out of the 20 accounts. Let X be the number of accounts in the sample that are in error. Is X binomial? If not, what distribution does it have? Explain. ... Problem 5-74 The Toyota Prius uses both gaso

Drawing Inferences from Large Samples

I need help with details on the following problem: The time it takes for a taxi to drive fro, the office to the airport was recorded on 40 occasions. It was found that x_bar = 47 minutes and s = 5 minutes. Give a) An estimate of μ = population mean time to drive. b) An approximate 95.4% error margin. Thanks

Statistical Inference

An agribusiness company currently uses one brand of commercial fertilizer. However, a new fertilizer is available that the manufacturer says will produce higher than average crop yields. Name the basic category of statistical inference tools the manufacturer would use to provide this information. Describe a hypothesis upon


A group of executives at a local company is considering introducing a new product into a market area. It is important to know the age characteristics of the people in the market area. a. If the executives with to calculate a number that would characterize the "center" of the age data, what statistical technique would you sugg

International Labor Wages

SCENARIO: The U.S. Bureau of Labor Statistics ( released hourly wage figures for western countries in 2000 in the manufacturing sector. The hourly wage was $24.01 in Germany, $22.00 in Japan, and $19.86 in the United States. PROBLEM: Suppose 40 manufacturing workers are selected randomly from across