T Test for Two Samples Means with Example Problem | Two-Tailed Test | Hypothesis Testing Statistics Video
T Test for Two Samples Means with Example Problem | Two-Tailed Test | Hypothesis Testing Statistics
The T-test is applied when it is believed that the two population means are equal hypothetically it implies using a T-test you can test the null hypothesis which states as the two population means are equal.
PROBLEM
Sample means of the sales of the shop in two towns are given with sample variance for 5 and 7 days in town A and town B respectively. It is required to conclude that the sales in the two towns are different at a 5% significance level.
SOLUTION
Step 1:
State the Null hypothesis: Means of two populations are the same
Stare the alternative hypothesis: Means of two populations are different
Step 2:
Write down the parameters given in the problem such as; values of sample means, sample variances, sample size, and significance level.
Step: 3
Write the equation of test statistic for the t-test to calculate the value of ‘t’.
Step: 4
Put the values of sample means, sample variances, and the sample size in the equation of test statistic for the t-test and calculate the value of ‘t’
Step: 5
Calculate the degrees of freedom, and find the critical value at a 5% significance level against the degrees of freedom from the ‘t’ distribution table.
Step: 6
Compare the mode of the calculated value of ‘t’ with the critical value of ‘t’. If the calculated value of ‘t’ is greater than the critical value of ‘t’ then reject the Null hypothesis, it implies the population means are different.
If the mode of the calculated value of ‘t’ is less than the critical value of ‘t’ then continue with the Null hypothesis, which implies the population means are the same.
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