In statistics, hypothesis testing used widely. A technical guess statement of any phenomenon occurring over the earth’s plane is said to be hypothesis. Hypothesis testing is a technique used to solve complicated statistical problems. T critical value is used to accept or reject the null hypothesis. In this post, we will cover all the basics of hypothesis testing and calculation of t value (critical value) with a lot of examples.
What is Hypothesis Testing?
A technical guess statement of any phenomenon occurring over the earth’s plane is said to be hypothesis. Hypothesis testing is a method for determining how reliably one can generalize observed findings in a sample under study to the larger population from which the sample was drawn. It’s used to evaluate the sample’s evidence and to create a framework for making population-related decisions.
The transformation of the study question into a null hypothesis, H0, and an alternative hypothesis, HA is the first stage in testing hypotheses. The null and alternative hypotheses are short explanations of two possible versions of “truth” concerning the relationship between the predictor of interest and the population outcome, usually in mathematical form.
There are six steps for calculating hypothesis testing.
- Hypothesis (null or alternative)
- Assumptions (measurement level of data)
- Confidence interval structure
- Rejection region
- Solution or calculation
- Conclusion
Hypothesis testing is used to determine if the null hypothesis (no difference, no effect) may be accepted or rejected. The research hypothesis can be accepted if the null hypothesis is rejected.
What is t value (critical value)?
The t value (crucial value) is the value that determines whether we keep or reject the null hypothesis. If the statistic value is greater than the x-axis, the null hypothesis is rejected; otherwise, the null hypothesis is accepted. An alternate hypothesis will be accepted if the null hypothesis is rejected.
In hypothesis testing, the t-value expresses the magnitude of the difference in terms of the variation in your sample data. The bigger the value of t, the more evidence there is that the null hypothesis is false.
The equation of t value can be written as,
T = (x – µ)/ (s / √n)
In this equation, s is used for standard deviation, n is the number of samples, x is the sample mean, and µ is the population mean.
T value can be calculated by using formula or table. If you want accurate result according to formula or table you can use t value calculator. we can find t values for one-tail or two-tail. T value have different results on one-tail or two-tail.
How to evaluate t value?
To evaluate t value, you must have a sound knowledge about degree of freedom and significance level. Degree of freedom is stated as the quantity of information that your data deliver and you can apply to estimate the values of unidentified population parameters. While the significance level which can also be known as alpha is defined as the probability of an event could have occurred by chance.
Example 1
A workshop wants to improve its sale of garments. The previous sales data specified the mean sale of 16 salesmen was Rs 700 per contract. After training, the investigated data showed an average sale of Rs 900 per contract. If the standard deviation is Rs 200, calculate the t value?
Solution
Step 1: Write the equation of t value.
t = (x – µ)/ (s/√n)
Step 2: Find values from given problem.
Sample mean = x = Rs 900
Population mean = µ = Rs 700
Standard deviation = s = Rs 200
n = 16
Step 3: Placed the values in the formula.
t = (x – µ)/ (s / √n)
t = (900 – 600) / (200/ √16)
t = 300 / (200/4)
= 300 / 50
t = 6
From t table 6 > 1.9432 at alpha = 0.05.
Hence training increases the sales.