Hypothesis testing - Business Statistics

                                         Hypothesis testing 
Statistical hypothesis testing is used to assess the strength of the evidence in a random sample against a stated null hypothesis concerning a population parameter. A null hypothesis is a conjecture about a population parameter that is stated as a mathematical equation.
To conduct the hypothesis test, we require a random sample of observed data. From that sample, we calculate a value for a statistic that is relevant for the hypothesis. 

Summary Hypothesis testing 

1. State the null and alternative hypothesis
2. Chose a test statistic that summarizes the observed data and is relevant to the null hypothesis
3. Calculate the test statistic from the random sample and calculate its p-value
4. Using the p-value, assess the strength of the evidence against the null hypothesis

In fixed level testing, a significance level is chosen prior to collecting the sample, and the following decision rule is used:

• If the p-value of the test statistic is less than or equal to the significance level (α), reject the null hypothesis
• If the p-value of the test statistic is greater than the significance level (α), fail to reject the null hypothesis

Steps in  Hypothesis testing

1. The first step is to specify the null hypothesis. For a two-tailed test, the null hypothesis is typically that a parameter equals zero although there are exceptions. A typical null hypothesis is μ₁ - μ₂ = 0 which is equivalent to μ₁ = μ₂. For a one-tailed test, the null hypothesis is either that a parameter is greater than or equal to zero or that a parameter is less than or equal to zero. If the prediction is that μ₁ is larger than μ₂, then the null hypothesis (the reverse of the prediction) is μ₂ - μ₁ ≥ 0. This is equivalent to μ₁ ≤ μ₂.
   
   
2. The second step is to specify the α level which is also known as the significance level. Typical values are 0.05 and 0.01.
   
   
3. The third step is to compute the probability value (also known as the p value). This is the probability of obtaining a sample statistic as different or more different from the parameter specified in the null hypothesis given that the null hypothesis is true.
   
   
4. Finally, compare the probability value with the α level. If the probability value is lower then you reject the null hypothesis. Keep in mind that rejecting the null hypothesis is not an all-or-none decision. The lower the probability value, the more confidence you can have that the null hypothesis is false. However, if your probability value is higher than the conventional α level of 0.05, most scientists will consider your findings inconclusive. Failure to reject the null hypothesis does not constitute support for the null hypothesis. It just means you do not have sufficiently strong data to reject it