Calculating p value
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When you perform a hypothesis test in statistics, a p-value helps you determine the significance of your results. ... The p-value is a number between 0 and 1 and interpreted in the following way: A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.
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P value
This document discusses p-values and their significance in statistical hypothesis testing. It defines a p-value as the probability of obtaining a result equal to or more extreme than what was observed assuming the null hypothesis is true. Lower p-values indicate stronger evidence against the null hypothesis. The document outlines the steps in hypothesis testing which include stating hypotheses, determining acceptable type I and type II error rates, selecting a statistical test to calculate a test statistic, determining the p-value, making inferences, and forming conclusions. It emphasizes that statistical significance does not necessarily imply real-world significance.
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This document discusses factors related to determining sample size for research studies. It defines key terms like sample size, population and importance of sample size. The selection of sample size involves planning the study, specifying parameters, choosing an effect size, and computing the sample size based on those factors. Sample size is influenced by expected effect size, study power, heterogeneity, error risk, and other variables. Dropouts from the sample during a study also impact sample size calculations. Proper determination of sample size is important for obtaining meaningful results and conducting ethical research.
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This document provides an overview of key concepts in biostatistics. It defines biostatistics as the application of statistical methods in the fields of biology, public health, and medicine. Some key points covered include:
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- Descriptive statistics like mean, median, and mode
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This document provides information about the Kruskal-Wallis H test, a non-parametric method for testing whether samples originate from the same distribution. It describes how the Kruskal-Wallis test is a generalization of the Mann-Whitney U test that allows comparison of more than two independent groups. The test works by ranking all data from lowest to highest and then summing the ranks for each group to calculate the test statistic H, which is compared to a chi-squared distribution to determine whether to reject or fail to reject the null hypothesis that all population medians are equal.
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This document provides an outline for a presentation on determining sample size. It discusses key concepts like what sample size is, why determining an appropriate sample size is important, and factors that affect sample size calculations like available resources, required accuracy, and study design. The presentation aims to help audiences understand how to determine sample sizes and how to apply the concept in research and studies.
Confidence intervals
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- When the sample size is small, a t-distribution rather than normal distribution is used to construct the confidence interval due to the unknown population standard deviation. The t-distribution is wider than the normal and accounts for additional uncertainty from an unknown standard deviation.
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P value
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- The types of data: qualitative, quantitative, discrete, continuous
- Descriptive statistics like mean, median, and mode
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- The process of determining sample size for studies based on factors like confidence interval, power, and allowable error.
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NULL AND ALTERNATIVE HYPOTHESIS.pptx
The document discusses null and alternative hypotheses.
The null hypothesis states that there is no relationship or difference between two variables and is what researchers aim to disprove. It is represented by H0 and can be rejected but not accepted.
The alternative hypothesis proposes an alternative theory to the null hypothesis by stating a relationship or difference does exist between variables. It is represented by H1 or Ha.
If the null hypothesis is rejected based on a low p-value, the alternative hypothesis is supported, meaning the results are statistically significant. Examples of null and alternative hypotheses are provided.
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The document defines key concepts in hypothesis testing such as critical value, significance level, p-value, type I and type II errors, and power. It states that the critical value divides the normal distribution into regions for rejecting or failing to reject the null hypothesis. The significance level corresponds to the critical region. A p-value less than 0.05 indicates the result is statistically significant. Type I error occurs when the null hypothesis is rejected when it is true, while type II error is failing to reject a false null hypothesis. Power is defined as 1 - β, where β is the probability of a type II error.
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The document provides an overview of hypothesis testing. It begins by defining a hypothesis test and its purpose of ruling out chance as an explanation for research study results. It then outlines the logic and steps of a hypothesis test: 1) stating hypotheses, 2) setting decision criteria, 3) collecting data, 4) making a decision. Key concepts discussed include type I and type II errors, statistical significance, test statistics like the z-score, and assumptions of hypothesis testing. Factors that can influence a hypothesis test like effect size, sample size, and alpha level are also covered.
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This document discusses sample size estimation and the factors that influence determining an appropriate sample size for research studies. It provides examples of calculating sample sizes based on prevalence of a disease, mean values, standard deviations, permissible errors, and confidence levels. The key points are:
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- Examples are provided to demonstrate calculating sample sizes based on prevalence of anemia, mean blood pressure values, and acceptable margins of error
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Confidence Interval Module
One of the key concepts of statistics enabling statisticians to make incredibly accurate predictions is called the Central Limit Theorem. The Central Limit Theorem is defined in this way:
· For samples of a sufficiently large size, the real distribution of means is almost always approximately normal.
· The distribution of means gets closer and closer to normal as the sample size gets larger and larger, regardless of what the original variable looks like (positively or negatively skewed).
· In other words, the original variable does not have to be normally distributed.
· This is because, if we as eccentric researchers, drew an almost infinite number of random samples from a single population (such as the student body of NMSU), the means calculated from the many samples of that population will be normally distributed and the mean calculated from all of those samples would be a very close approximation to the true population mean. It is this very characteristic that makes it possible for us, using sound probability based sampling techniques, to make highly accurate statements about characteristics of a population based upon the statistics calculated on a sample drawn from that population.
· Furthermore, we can calculate a statistic known as the standard error of the mean (abbreviated s.e.) that describes the variability of the distribution of all possible sample means in the same way that we used the standard deviation to describe the variability of a single sample. We will use the standard error of the mean (s.e.) to calculate the statistic that is the topic of this module, the confidence interval.
The formula that we use to calculate the standard error of the mean is:
s.e. = s / √N – 1
where s = the standard deviation calculated from the sample; and
N = the sample size.
So the formula tells us that the standard error of the mean is equal to the
standard deviation divided by the square root of the sample size minus 1.
This is the preferred formula for practicing professionals as it accounts for errors that may be a function of the particular sample we have selected.
THE CONFIDENCE INTERVAL (CI)
The formula for the CI is a function of the sample size (N).
For samples sizes ≥ 100, the formula for the CI is:
CI = (the sample mean) + & - Z(s.e.).
Let’s look at an example to see how this formula works.
* Please use a pdf doc. “how to solve the problem”, I have provided for you under the “notes” link.
Example 1
Suppose that we conducted interviews with 140 randomly selected individuals (N = 140) in a large metropolitan area. We assured these individuals that their answers would remain confidential, and we asked them about their law-breaking behavior. Among other questions the individuals were asked to self-report the number of times per month they exceeded the speed limit. One of the objectives of the study was to estimate (make an inference about) the average nu.
Elements of inferential statistics
1. The document discusses key concepts in inferential statistics including point estimation, interval estimation, hypothesis testing, types of errors, p-values, power, and one-tailed and two-tailed tests.
2. It explains that inferential statistics allows generalization from a sample to a population and includes estimation of parameters and hypothesis testing.
3. Common statistical techniques covered are confidence intervals, which provide a range of values that likely contain the true population parameter, and hypothesis testing, which evaluates theories about populations.
Week 6 project part b
This document discusses four hypothesis tests and confidence intervals:
1) A z-test finds the average annual income was less than $50,000 based on a p-value less than 0.05.
2) A z-test for proportion finds insufficient evidence the proportion of urban customers exceeds 40% with a p-value greater than 0.05.
3) A z-test finds insufficient evidence the average years lived in a home is less than 13 based on a p-value greater than 0.05.
4) A z-test finds the average credit balance for suburban customers is more than $4,300 based on a p-value less than 0.05.
Stats chapter 10
This document provides an overview of confidence intervals. It defines key terms like statistical inference, confidence level, and margin of error. It explains how to construct confidence intervals for means using the z-distribution when the population standard deviation is known, and using the t-distribution when it is unknown. It also covers how to estimate population proportions using the normal distribution. Examples are provided to demonstrate how to use the PANIC method to set up and calculate confidence intervals.
Null hypothesis 2
The document discusses key concepts related to p-values and significance testing. It defines a p-value as the likelihood that a difference detected is due to chance rather than a true effect. A difference is considered statistically significant if the p-value is less than 0.05, meaning there is less than a 5% chance the difference is due to random error. The document also discusses critical values, which are numerical cut-offs used to determine whether to reject or retain the null hypothesis, and types I and II errors that can occur in significance testing.
Intro to data science
This document provides an overview and agenda for a hands-on introduction to data science. It includes the following sections: Data Science Overview and Intro to R (90 minutes), Exploratory Data Analysis (60 minutes), and Logistic Regression Model (30 minutes). Key topics that will be covered include collecting and analyzing data to find insights to help decision making, predicting problems before they occur, using analytics to improve operations and innovations, and examples of predicting loan defaults. Machine learning concepts such as supervised and unsupervised learning and common machine learning models will also be introduced.
Introduction To Data Science Using R
This document provides an overview and agenda for a hands-on introduction to data science. It includes the following sections: Data Science Overview and Intro to R (90 minutes), Exploratory Data Analysis (60 minutes), and Logistic Regression Model (30 minutes). The document then covers key concepts in data science including collecting and analyzing data to find insights to help decision making, using analytics to improve operations and innovations, and predicting problems before they occur. Machine learning and statistical techniques are also introduced such as supervised and unsupervised learning, parameters versus statistics, and calculating variance and standard deviation.
Hypothesis testing
This document discusses hypothesis testing, which involves drawing inferences about a population based on a sample from that population. It outlines the key elements of a hypothesis test, including the null and alternative hypotheses, test statistics, critical regions, significance levels, critical values, and p-values. Type I and Type II errors are explained, where a Type I error involves rejecting the null hypothesis when it is true, and a Type II error involves failing to reject the null when it is false. The power of a hypothesis test is defined as the probability of correctly rejecting the null hypothesis when it is false. Controlling type I and II errors involves considering the significance level, sample size, and population parameters in the null and alternative hypotheses.
01 unidad i ho p
The document discusses hypothesis testing for a proportion. It provides the steps to conduct a hypothesis test on a proportion:
1. State the null and alternative hypotheses, with the null hypothesis claiming the population proportion is equal to a specific value.
2. Select the significance level.
3. Calculate the test statistic, which is a z-score comparing the sample proportion to the null hypothesized proportion.
4. Determine if the test statistic falls in the critical region, rejecting the null hypothesis if it does.
As an example, it tests the claim that a fertility method increases the chance of having a girl using sample data and finds strong evidence to reject the null hypothesis that the population proportion is 0.5
What is Simple Linear Regression and How Can an Enterprise Use this Technique...
What is Simple Linear Regression and How Can an Enterprise Use this Technique...Smarten Augmented Analytics
(1) The document provides an introduction to simple linear regression, including definitions of key terms like predictors, target variable, coefficients, and error terms. (2) It presents an example of simple linear regression analysis to predict yield based on temperature. (3) The outputs like regression statistics, line fit plot, and residual plot are interpreted to evaluate the relationship between the variables and check assumptions.Similar to Calculating p value (20)
Statistical tests of significance and Student`s T-Test
Statistical tests of significance and Student`s T-Test
Confidence Interval ModuleOne of the key concepts of statist.docx
Confidence Interval ModuleOne of the key concepts of statist.docx
What is Simple Linear Regression and How Can an Enterprise Use this Technique...
What is Simple Linear Regression and How Can an Enterprise Use this Technique...
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Willens's syndrome.pptx
A 57-year-old woman was admitted to the hospital with chest pain. Electrocardiograms and troponin levels were normal. Intravascular ultrasound was performed before placing a stent in the left main coronary artery and left anterior descending artery to treat a blockage. The minimum lumen area increased to 4.24mm x 4.13mm after stenting.
Intensive care of congenital heart disease.pptx
Congenital defects can put a strain on the heart, causing it to work harder. To stop your heart from getting weaker with this extra work, your doctor may try to treat you with medications. They are aimed at easing the burden on the heart muscle. You need to control your blood pressure if you have any type of heart problem.
Management of Hypetension.pptx
Changing your lifestyle can help control and manage high blood pressure. Your health care provider may recommend that you make lifestyle changes including:
Eating a heart-healthy diet with less salt
Getting regular physical activity
Maintaining a healthy weight or losing weight
Limiting alcohol
Not smoking
Getting 7 to 9 hours of sleep daily
CRISPR and cardiovascular diseases.pdf
CRISPR technologies have progressed by leaps and bounds over the past decade, not only having a transformative effect on
biomedical research but also yielding new therapies that are poised to enter the clinic. In this review, I give an overview of (i)
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cell models, and functional screens, and (iii) emerging therapeutic applications for patients with cardiovascular diseases, focusing on the examples of Hypercholesterolemia, transthyretin amyloidosis, and Duchenne muscular dystrophy.
Pacemaker Pocket Infection After Splenectomy
This case report describes a patient who underwent seven operations over one year to treat recurrent pacemaker pocket infections. The patient had undergone a splenectomy seven years prior due to a splenic rupture from a traffic accident. This left the patient immunocompromised and at higher risk for infection. The patient later required a pacemaker implantation for complete heart block. The pacemaker pocket developed repeated infections, likely due to the patient's asplenic state impairing immunity. The infections were difficult to treat due to multiple complicating factors, including an abandoned pacemaker lead and reuse of a sterilized pacemaker. This highlights the influence of patient factors like asplenia on procedural outcomes like pacemaker implantation.
Piccolo Duct Occluder.pdf
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Accidental misplacement of the limb lead electrodes is a common cause of ECG abnormality and may simulate pathology such as ectopic atrial rhythm, chamber enlargement or myocardial ischaemia and infarction
A Case of Device Closure of an Eccentric Atrial Septal Defect Using a Large D...
Device closure of an eccentric atrial septal defect can be challenging and needs technical modifications to avoid unnecessary complications. Here, we present a case of a 45-year-old woman who underwent device closure of an eccentric defect with a large device. The patient developed pericardial effusion and left-sided pleural effusion due to injury to the junction of right atrium and superior vena cava because of the malalignment of the delivery sheath and left atrial disc before the device was pulled across the eccentric defect despite releasing the left atrial disc in the left atrium in place of the left pulmonary vein. These two serious complications were managed conservatively with close monitoring of the case during and after the procedure.
Arrythmia-IV.pptx
1) Bradycardia can be caused by abnormalities in the conduction system or autonomic nervous system. The conduction system includes the sinus node, AV node, His-Purkinje system and different types of heart block can occur when impulses are blocked at different locations.
2) There are three main types of AV block - first degree, second degree (Mobitz types I and II), and third degree. High grade AV block involves blockage of two or more consecutive impulses.
3) Third degree or complete heart block results in complete dissociation between the atria and ventricles with independent pacemakers. It can occur at the AV node or below in the His-Purkin
Arrythmia-III.pptx
1. Bradycardia is defined as a resting heart rate below 50 beats per minute. It can be physiological or pathological.
2. Sinus bradycardia originates from the sinus node and has a normal P wave morphology with a prolonged PR interval. It can be caused by increased vagal tone, medications, or hypothyroidism.
3. Sick sinus syndrome is characterized by sinus bradycardia, sinus arrest, or combinations of sinus node and AV node dysfunction. It may involve intermittent bradycardia and tachycardia. Pacemaker implantation is usually treatment.
Arrythmia-II.pptx
This document discusses ventricular arrhythmias including their origins, characteristics, classifications, and causes. It provides details on:
- The sites of origin for supraventricular tachycardia (SVT) and ventricular arrhythmias.
- Characteristics that distinguish SVT from ventricular arrhythmias such as QRS width.
- Classifications of ventricular arrhythmias including premature ventricular complexes, ventricular tachycardia, fibrillation, and electrical storm.
- Causes and characteristics of different types of ventricular tachycardia such as monomorphic VT, polymorphic VT, and torsades de pointes.
- Investigations and treatments for ventricular arrhythmias including cardiac imaging
Arrythmia-I.pptx
This document provides information on supraventricular tachycardia (SVT), including:
- The anatomy and conduction system of the heart that is relevant to SVT.
- The mechanisms that can cause cardiac arrhythmias, including disorders of impulse formation, conduction, and combinations of the two.
- Characteristics used to classify different types of arrhythmias based on rate, rhythm, site of origin, and QRS morphology.
- Specific types of SVT like atrial fibrillation, AV nodal reentry tachycardia, and accessory pathway mediated tachycardias.
- Methods for diagnosing and treating SVT such as electrophysiology studies, catheter ablation
Trio of Rheumatic Mitral Stenosis, Right Posterior Septal Accessory Pathway a...
A 57-year-old male presented with recurrent palpitations. He was diagnosed with rheumatic mitral stenosis, right posterior septal accessory pathway and atrial flutter. An electrophysiological study after percutaneous balloon mitral valvotomy showed that the palpitations were due to atrial flutter with right bundle branch aberrancy. The right posterior septal pathway was a bystander because it had a higher refractory period than the atrioventricular node.
Anticoagulation therapy during pregnancy
This document discusses anticoagulation therapy options during pregnancy for different cardiac conditions. It notes that vitamin K antagonists (VKAs) should be avoided in the first trimester due to risk of embryopathy but can be used in the second and third trimester with risks of 0.7-2% of foetopathy. Unfractionated heparin does not cross the placenta but its use throughout pregnancy is not recommended due to risk of foetopathy. Low molecular weight heparin is considered the safest option for anticoagulation in weeks 6-12 when risk of embryopathy is a concern and has not been associated with risk of foetopathy. Fondaparinux use should be limited
Coronary guidewire
Percutaneous balloon dilatation, first described by
Andreas Gruentzig in 1979, was initially performed
without the use of guidewires.1 The prototype
balloon catheter was developed as a double lumen
catheter (one lumen for pressure monitoring or
distal perfusion, the other lumen for balloon inflation/deflation) with a short fixed and atraumatic
guidewire at the tip. Indeed, initially the technique
involved advancing a rather rigid balloon catheter
freely without much torque control into a coronary
artery. Bends, tortuosities, angulations, bifurcations,
and eccentric lesions could hardly, if at all, be negotiated, resulting in a rather frustrating low procedural success rate whenever the initial limited
indications (proximal, short, concentric, noncalcified) were negated.2 Luck was almost as
important as expertise, not only for the operator,
but also for the patient. It is to the merit of
Simpson who, in 1982, introduced the novelty of
advancing the balloon catheter over a removable
guidewire, which had first been advanced in the
target vessel.3 This major technical improvement
resulted overnight in a notable increase in the procedural success rate. Guidewires have since evolved
into very sophisticated devices.
Intracoronary optical coherence tomography
Optical coherence tomography-guided algorithm for percutaneous coronary intervention. Vessel diameter should be assessed using the external elastic lamina (EEL)-EEL diameter at the reference segments, and rounded down to select interventional devices (balloons, stents). If the EEL cannot be identified, luminal measures are used and rounded up to 0.5 mm larger for selection of the devices. Optical coherence tomography (OCT)-guided optimisation strategies post stent implantation per EEL-based diameter measurement and per lumen-based diameter measurement are shown. For instance, if the distal EEL-EEL diameter measures 3.2 mm×3.1 mm (i.e., the mean EEL-based diameter is 3.15 mm), this number is rounded down to the next available stent size and post-dilation balloon to be used at the distal segment. Thus, a 3.0 mm stent and non-compliant balloon diameter is selected. If the proximal EEL cannot be visualised, the mean lumen diameter should be used for device sizing. For instance, if the mean proximal lumen diameter measures 3.4 mm, this number is rounded up to the next available balloon diameter (within up to 0.5 mm larger) for post-dilation. MLA: minimal lumen area; MSA: minimal stent area;NC: non-compliant
Brugada syndrome
Brugada syndrome (BrS) is an inherited cardiac disorder,
characterised by a typical ECG pattern and an increased
risk of arrhythmias and sudden cardiac death (SCD).
BrS is a challenging entity, in regard to diagnosis as
well as arrhythmia risk prediction and management.
Nowadays, asymptomatic patients represent the majority
of newly diagnosed patients with BrS, and its incidence
is expected to rise due to (genetic) family screening.
Progress in our understanding of the genetic and
molecular pathophysiology is limited by the absence
of a true gold standard, with consensus on its clinical
definition changing over time. Nevertheless, novel
insights continue to arise from detailed and in-depth
studies, including the complex genetic and molecular
basis. This includes the increasingly recognised
relevance of an underlying structural substrate. Risk
stratification in patients with BrS remains challenging,
particularly in those who are asymptomatic, but recent
studies have demonstrated the potential usefulness
of risk scores to identify patients at high risk of
arrhythmia and SCD. Development and validation of
a model that incorporates clinical and genetic factors,
comorbidities, age and gender, and environmental
aspects may facilitate improved prediction of disease
expressivity and arrhythmia/SCD risk, and potentially
guide patient management and therapy. This review
provides an update of the diagnosis, pathophysiology
and management of BrS, and discusses its future
perspectives.
A roadmap for the human development
The Human Developmental Cell Atlas (HDCA) initiative, which is part of the Human Cell Atlas, aims to create a comprehensive reference map of cells during development. This will be critical to understanding normal organogenesis, the effect of mutations, environmental factors and infectious agents on human development, congenital and childhood disorders, and the cellular basis of ageing, cancer and regenerative medicine. Here we outline the HDCA initiative and the challenges of mapping and modelling human development using state-of-the-art technologies to create a reference atlas across gestation. Similar to the Human Genome Project, the HDCA will integrate the output from a growing community of scientists who are mapping human development into a unified atlas. We describe the early milestones that have been achieved and the use of human stem-cell-derived cultures, organoids and animal models to inform the HDCA, especially for prenatal tissues that are hard to acquire. Finally, we provide a roadmap towards a complete atlas of human development.
Intra aortic balloon pump
The treatment of patients with advanced acute heart failure is still challenging.
Intra-aortic balloon pump (IABP) has widely been used in the management of
patients with cardiogenic shock. However, according to international guidelines, its
routinary use in patients with cardiogenic shock is not recommended. This recommendation is derived from the results of the IABP-SHOCK II trial, which demonstrated
that IABP does not reduce all-cause mortality in patients with acute myocardial infarction and cardiogenic shock. The present position paper, released by the Italian
Association of Hospital Cardiologists, reviews the available data derived from clinical
studies. It also provides practical recommendations for the optimal use of IABP in
the treatment of cardiogenic shock and advanced acute heart failure.
Left ventricular false tendons
Left ventricular false tendons (LVFTs) are fibromuscular
structures, connecting the left ventricular
free wall or papillary muscle and the ventricular
septum.
There is some discussion about safety issues during
intense exercise in athletes with LVFTs, as these
bands have been associated with ventricular arrhythmias
and abnormal cardiac remodelling. However,
presence of LVFTs appears to be much more common
than previously noted as imaging techniques
have improved and the association between LVFTs
and abnormal remodelling could very well be explained
by better visibility in a dilated left ventricular
lumen.
Although LVFTsmay result in electrocardiographic abnormalities
and could form a substrate for ventricular
arrhythmias, it should be considered as a normal
anatomic variant. Persons with LVFTs do not appear
to have increased risk for ventricular arrhythmias or
sudden cardiac death.
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Calculating p value
- 2. Alpha (α) • Lesser area remained beyond the e line of critical line either on left or right side of it ,lesser is the possibility that the observation is chance finding or by sampling error ,rather there is true difference population mean and sample mean • Alpha value =area under curve to the right or left to critical line • The value of alpha says in what percent of cases the observation is merely by chance /sampling error • Smaller is alpha value ,larger area is found under non alpha area ,that mean we are more and more confident that there is difference between population mean and sample mean • Critical line =z or t value of sample of sample under study • That is P-value along with mention of 95% CI interval is more meaningful
- 3. Green line is critical value of z or t =sample statistic 95% CI interval=.95 x area under curve =95% time we confident that the association is not by chance or sampling error
- 4. • Lesser its value ,it says lesser the possibility that your observed mean is by chance or by sampling error rather by true association =null hypothesis is not true =there is difference between population mean and your sample mean
- 5. KEY WORDS STATISTIC :MEAN ,MEDIAN ,MODE ,Z AND T VALUE OF YOUR RESEARCH Parameter : MEAN ,MEDIAN ,MODE ,Z AND T VALUE OF population Null hypothesis :There is no difference between parameter and statistic,α≥0.05 Alternative hypothesis : There is a difference between parameter and statistic: α≤0.05=The observation by chance or sampling error is up to the extent less than 0.05 . P value :0.05% AREA under bell shaped curve =rejected area =any value which would fall in this area would be only by chance or sampling error .Lesser the value of P ,lesser it is due to chance or sampling error 95% CI =0.95 area under the bell shaped curve when the entire area under curve is =1
- 6. Steps • One tailed : • sample mean is bigger than population mean • sample mean is smaller than population mean • Two tailed :sample mean(statistic) is not same bigger than population mean(parameter)
- 7. When to calculate alpha(α) using z statistic of your sample? When you know the parameter called standard deviation of population Otherwise use t test method to get alpha value
- 8. HYPOTHESIS TESTING STAGES STATE NULL AND ALTERNATIVE HYPOTHESIS Choose the level of significance (alpha) Find the critical value(z or t) of your sample Find the test sample statistic :Z or t of the sample Draw your conclusion :H0 OR HA is true
- 9. Some practical links one tailed Two tailed
- 10. You are welcome to comments