Essays on Test Statistic

Statistical hypothesis testing is a very important concept in statistics. There are steps to be followed in hypothesis testing, as shown below (Eberly College of Science, n.d.) Formulation of the Null Hypothesis – this step involves stating of the null hypothesis, which states equality between the hypothesized value and a predicted value. In this case, it is the opposite of the alternative hypothesis.

H0: The average salary for all jobs in Minnesota is greater than or equal to $65,000.

H0: x ≥$65,000 Formulation of the Alternative Hypothesis –the alternative hypothesis is the opposite of the null hypothesis, which states that a value is less than, greater than, or not equal to a certain value. This ...

One of the contentious topics that is sure to spark discussion nowadays is the issue of the difference between natural US citizens and immigrants. Some feel that immigrants are different from natural US citizens in some aspects, and these differences lead to ruin of the American economy and society. Others maintain that there is no significant difference between the two and as such they should be treated more or less the same. Immigrants and US citizens can be compared in different ways, one of which being the topic of domestic violence. Domestic violence is an umbrella term for any ...

Literature Review of a Two-Sample Test

Lee, J. S., Cox, D. D., & Follen, M. (2015). A Two Sample Test for Functional

22(2), 121-135. doi:10.5351/csam.2015.22.2.121. The study of “A Two Sample Test for Functional Data” was published in the journal Communications for Statistical Applications and Methods. The study was an extensive simulation, which portrays proposed test works in comparison to other methods under a variety of alternatives. This is one of the best methods for testing all alternatives. It is an application to demonstrate real-world data and the applicability for this particular method. For the simulations they used MATLAB except for the use of smoothing ...

Abstract

Mathematical statistics is a science that develops mathematical methods and systematic use of statistics for scientific and practical conclusions. In many of his areas of mathematical statistics is based on probability theory to gauge the reliability and accuracy of the findings made on the basis of limited statistical data (eg, to estimate the required sample size to produce the results desired accuracy in a sample survey). Allocate descriptive statistics, theory of estimation and hypothesis testing theory. Descriptive statistics is a set of empirical methods used for the visualization and interpretation of data (calculation of sample characteristics, tables, charts, graphs, ...

Question 1

Critical value method involves determining the likeliness or unlikeliness by determining whether the test statistic observed is more extreme than the null value or not. P-value is the probability of getting a value of sample test statistic that is far from the expected to be observed if null hypothesis holds true.

Question 2

F distribution is a ratio of two chi square random variables. The variance has a tendency to match the chi square distribution if one contains a normal random variable. It is used to determine if two variances are equal and to analyze variance and covariance figures. T distribution approximates the standard normal. ...

Type 1 and Type II Errors

The fundamental goal of research aims at testing the truthfulness of the null hypothesis. However, type 1 and type 2 errors may result from the process of testing the hypothesis. These errors negate the results of the study, consequently; this means that the results do not reflect the true condition. Type 1 error results from rejecting a true null hypothesis, while type 2 error results when a false-null hypothesis is accepted. For example, supposing that the research hypothesis is that drug A improves brain capacity for schizophrenia patients above 60 years. If a study is conducted to establish whether drug A is ...

The hypothesis test includes five distinct steps that may be followed in a specific order. In the first step, the researcher identifies a hypothesis that he would like to prove or disprove. The researcher will also formulate the alternative hypothesis which would be tested in case the original hypothesis does not stand true. In the second step, the researcher collects a random sample from the population which he would measure for the purpose of his study. Consequently, as a result of the second step, the relevant sample test statistic would be computed. Moving on to the third step, the researcher’s task is ...

CHAPTER 3: RESEARCH METHODOLOGY

3.1 Research Design The research design is a procedural plan adopted by the researcher to answer research questions objectively, accurately, validly and economically. In general, the research design plays two key roles. First, it aids in the identification and development of logical arrangements and procedures required to undertake a study. Second, the design lays emphasis on the quality (objectivity, validity and accuracy) of the underlying procedures. When conducting research, it is vital to note that the research design is distinct from the method through which data are collected. In general, there are a number of ways in which research designs ...

- A 95% confidence interval for the mean income of shop assistants in a certain city is found to be (£12,000, £15,000). Explain briefly what this means. Would a 99% confidence interval be better than a 95% one? Justify your answer. ANS – It means that there is 95% probability that the value of the parameter i.e. individual incomes of different shop assistants shall lie within the range of £12,000 to £15,000. Yes, 99% confidence level is better than a 95% one as it increases the probability of the incomes of different shop assistants to lie within the defined ...

Question 1

Steps of hypothesis testing Here, the researcher identifies his population of interest, value of the parameter which in this case is hypothesized and the parameter of the variable he intends to investigate. This variable can be categorical, continuous or discrete. The variable will define which statistical test will be suitable on the collected data set. - Specify alternative and null hypotheses. Here, the researcher states his research question in terms of alternative hypotheses or null hypotheses. Null hypotheses is a positive while alternative hypotheses is negative. It also involves selecting a significance level and evaluate the assumptions ...

[Date (May 23, 2013)]

- Introduction to alcohol consumption Alcohol consumption is taken as a leisure activity among many people across the world. There are many forms of alcohol available depending on the level of alcohol content and the manufacturing process used. Based on the alcohol content, it is classified as wines, spirits and beer while under manufacturing processes it is classified as commercial and traditional brew. Commercial alcohol (manufactured in industries) is a legal drink worldwide while the traditional brew is outlawed in majority of the countries. The question on the effect of alcohol on the behaviour of human ...

1.

Solution:

(a)

The 95% confidence interval is

We calculated it, it’s

So the 95% confidence interval for the average waiting time for the ride is (53.95, 70.85) (b)

The confidence interval means the probability that the average waiting time for the ride is between 53.95 minutes and 70.85 minutes is 0.95.

(c)

Because 60 is within (53.95, 70.85), so the park need to employ more Staff.

2.

Solution:

(a) The distribution of o is Z distribution.

The 90% confidence interval for the portion is

We calculate it, it’s

So a 90% confidence interval for the portion of 18-22 year olds who drank excessively before they were 18 is (0.607, 0.659). (b)

The confidence interval means the portion of 18-22 year olds who drank excessively before they were 18 is between 0.607 and 0.659 is 0.90.

3.

Solution:

(a)

The max error =

So 

So, the sample size needed is 86.

(b)

The max error of proportion is =

So

Because

So, so the sample size needed is 475. 4.

Solution:

(a)-(b)

The null hypothesis:

The alternative hypothesis: The test statistic = The p-value = P(Z1.768) = 0.077>0.05, so we can’t reject the null hypothesis, ...