Hypothesis tests are normally done for one and two samples. For one sample, researchers are often interested in whether a population characteristic such as the mean is equivalent to a certain value. For two samples, they may be interested in whether the true means are different. Statistical hypothesis tests depend on a statistic designed to measure the degree of evidence for various alternative hypotheses. The process of hypothesis testing consists of following procedure:
Basically, hypothesis testing involves on examination based on sample evidence and probability theory to determine whether hypothesis is reasonable statement. A hypothesis refers to the statement or claim about the whole population. A sample is taken out from the population and analysed. Accordingly, in hypothesis testing, hypothesis or claim is made about whole population, sample is taken out from the population and analysed. Finally, the results of analysis are used to decide whether claim made is reasonable to be accepted as true (Vohra, 1929).
Elements of a hypothesis test:
Another type of hypothesis is One and twotailed alternative hypotheses. A onetailed (or onesided) hypothesis specifies the direction of the association between the predictor and outcome variables. A onetailed hypothesis has the statistical advantage of permitting a smaller sample size as compared to that permissible by a twotailed hypothesis. Unfortunately, onetailed hypotheses are not always appropriate.
Figure: Hypothesis testing

Data Analysis Outcome 

In population 
Accept Null Hypothesis 
Reject Null Hypothesis 
Null Hypothesis True 
Correct Decision 
Type I Error 
Null Hypothesis False 
Type II Error 
Correct Decision 
Errors in hypothesis testing: It may be observed from the way hypothesis for a test are formulated, the null and alternate hypothesis are competing statement about the true state of nature.
Type I error, also called "false positive": The error of rejecting a null hypothesis when it is actually true. In other words, this is the error of accepting an alternative hypothesis (the real hypothesis of interest) when the results can be attributed to chance. Plainly speaking, it occurs when we are observing a difference when in truth there is none (or more specifically  no statistically significant difference). So the probability of making a type I error in a test with rejection region R is 0, P (R  H0 is true).
Type II error, also termed as a "false negative": The error of not rejecting a null hypothesis when the alternative hypothesis is the true state of nature. This is the error of failing to accept an alternative hypothesis when researcher do not have adequate power. Plainly speaking, it occurs when we are failing to observe a difference when in truth there is one. So the probability of making a type II error in a test with rejection region R is 1P(R Ha is true) − P R Ha. The power of the test can be P (R  Ha is true).
Table: Difference in type 1 and type 2 errors:
Type 1 Error 
Type 2 Error 










Reducing Type I Errors: Prescriptive testing is used to increase the level of confidence, which in turn reduces Type I errors. The chances of making a Type I error are reduced by increasing the level of confidence.
Reducing Type II Errors: Descriptive testing is used to better describe the test condition and acceptance criteria, which in turn reduces Type II errors. This increases the number of times we reject the Null hypothesis – with a resulting increase in the number of Type I errors (rejecting H0 when it was really true and should not have been rejected). Therefore, reducing one type of error comes at the expense of increasing the other type of error.
Testing hypotheses for difference between means: Testing differences two or more means is commonly used in experimental research. The statistical technique used when testing more than two means is called the analysis of variance. The hypothesis testing procedure for differences in means differ depending on the following criteria (Aaker, 2008):
The logic behind the hypotheses test and the basic concept of the tests remain the same for above conditions.
Testing hypotheses for difference between proportions: It is normally important to test the difference between two population proportions. The first step in hypothesis test for difference in proportion is to calculate the standard error of the proportion using the hypothesized value of defect free and defective items (Aaker, 2008).
Pitfalls of hypothesis testing: In hypothesis testing, Statistical significance does not imply a causeeffect relationship and it interpret results in the context of the study design. Hypothesis testing is dependent on concentrations tested. Statistical power is influenced by variability. In Hypothesis testing, research is unable to calculate confidence intervals. It is confounded by poorly behaved data and frequently need to use nonparametric statistical methods.
To summarize, Hypothesis testing also called significance testing is a technique for testing a claim or hypothesis about a parameter in a population, using data measured in a sample. In this method, researcher test some hypothesis by determining the likelihood that a sample statistic could have been selected, if the hypothesis regarding the population parameter were true. The hypotheses are specified, an αlevel is chosen, a test statistic is calculated, and it is reported whether H0 and H1 is accepted. In practice, it may happen that hypotheses are suggested by the data, the choice of αlevel may be ignored, more than one test statistic is calculated, and many modifications to the formal procedure may be made (Berger, 1982). It is documented that hypothesis testing enables researcher to quantify the degree of uncertainty in sampling variation, which may account for the results that deviate from the hypothesized values in a particular study.