It is a hypothesis which states that there is no difference between the procedures and is denoted by H0. The following test of hypothesis can be conducted from the table above:
Test Statistic: It is the random variable X whose value is tested to arrive at a decision. The Central Limit Theorem states that for large sample sizes (n > 30) drawn randomly from a population, the distribution of the means of those samples will approximate normality, even when the data in the parent population are not distributed normally. A z statistic is usually used for large sample sizes (n > 30), but often large samples are not easy to obtain, in which case the t-distribution can be used. The population standard deviation s is estimated by the sample standard deviation, s.
Rejection Region: It is the part of the sample space (critical region) where the null hypothesis H0 is rejected. The size of this region is determined by the probability (a) of the sample point falling in the critical region when H0 is true. a is also known as the level of significance, the probability of the value of the random variable falling in the critical region. Also it should be noted that the term "Statistical significance" refers only to the rejection of a null hypothesis at some level a. It implies only that the observed difference between the sample statistic and the mean of the sampling distribution did not occur by chance alone.
The critical t value is obtained according to the degrees of freedom
The resulting t test values are shown in this table:
t-test: Two-Sample Assuming Equal Variances
Mean 6.6539 8.6874
Variance 0.2124 0.2988
Observations 10 10
Pooled Variance 0.2556
Hypothesized Mean Difference 0
Degrees of freedom