Hypothesis Testing | Importance of Hypothesis Testing | Examples of Hypothesis Testing | Two Sample Hypothesis Test | Business Statistics
What do you mean by hypothesis testing?
Hypothesis testing is one of the statistical methods which use experimental data for making statistical decisions. We make certain kinds of assumptions or predictions about the population parameter which is regarded as hypothesis testing. If there is a need to test the relationship between two variables then hypothesis testing is preferred.
Why is hypothesis testing important?
In an organization, on daily basis managers make various types of decisions that affect the efficiency, productivity as well as growth of their companies. Many organizations generally collect data from various sources in order to monitor their growth and progress as well as to be competitive than other companies and make better rational decisions.
The data that is collected cannot provide a clear picture of decision making and is needed to be critically analyzed in order to interpret it in the right way (Mohan, 2016). The data that is collected can be analyzed with the help of hypothesis testing.
What is an example of hypothesis testing?
For example, there is a company named Rater who wants to increase its sales wants to increase sales by introducing a new marketing campaign. Rater Company uses that marketing campaign around one region in the country. Rater Company collects the data in order to find out whether the marketing campaign introduced became effective or not.
The Rater Company will be only continuing the new marketing campaign at a national level if the company becomes sure that the sales are going to increase by 30%.In this case, hypothesis testing can be used on the basis of the sample selected on a particular region selected. If the results are interpreted properly then it helps the company to make a strategic rational decision. When it comes to testing a hypothesis, the company must develop a null hypothesis (Ho) and the alternative hypothesis (H1). Along with this, the company must define what statistic will be used as well as identify the level of significance.
Two-sample hypothesis testing
Two-sample hypothesis testing is a statistical analysis designed to test if there is a difference between two means from two different populations.
Illustration: Two-Sample Hypothesis Testing
Numerical illustration of CVS Pharmacy located on US 17 in Murrells Inlet.
Numerical Solution:
Given;
- Population Mean business volume of US 17 = µ_{1}
- Population Mean business volume of SC 707 = µ_{2}
- Sample number of observation for US 70 = n_{1}=25
- Sample number of observation for SC 707 = n_{2}=25
- Sample standard derivation of US 70 store = S_{1}
- Sample standard derivation of SC 707 store = S_{2}
- The sample mean business volume of US 17 = X̅_{1}
- The sample mean business volume of SC 707 =X̅_{2}
- Variable US 17 = X_{1}
- Variable SC 707 = X_{2}
- Level of significance (α) = 0.05
- Degree of freedom (df) = n_{1}+n_{2}-2 =48
Therefore, t_{α}, df =1.677
Hypothesis testing:
H_{o}: US 17 store has no more business volume than the SC 707 store. i.e., µ_{1}≤ µ_{2}
H_{1}: US 17 store has more business volume than the SC 707 store. i.e., µ_{1}> µ_{2}. (One-tail test)
T-Test: Two-Sample Hypothesis test assuming Equal variances
| Variable 1 | Variable 2 |
Mean | 11.48 | 8.68 |
Variance | 27.17667 | 14.14333 |
Observations | 25 | 25 |
Pooled Variance | 20.66 | |
Hypothesized Mean Difference | 0 | |
df | 48 | |
t Stat | 2.17795 | |
P(T<=t) one-tail | 0.017177 | |
t Critical one-tail | 1.677224 | |
P(T<=t) two-tail | 0.034355 | |
t Critical two-tail | 2.010635 |
Findings:
From the above calculations for the T-Test Two Sample Hypothesis test assuming Equal variances using excel, t_{cal} is 2.17795 and given in the question the critical value of one-tailed t-statistic at 0.05 level of significance is 1.667. Here t_{cal} >t_{critical} which indicates that the null hypothesis is rejected and the alternate hypothesis is accepted.
Conclusion:
From the overall analysis and conclusions, we can say that the US17 store has more business volume than that of the SC707 store at 0.05 level of significance based on the vehicle counts.