Independent Sample T-Test Example Problems With Solutions Pdf
If you are a statistics student, you might have heard about independent sample t-test. In statistics, a t-test is used to compare two sets of data from different populations. Independent sample t-test, also known as two-sample t-test, is a type of t-test used to compare two independent groups. In this article, we are going to discuss independent sample t-test example problems with solutions pdf that will help you understand this statistical test better.
What is Independent Sample T-Test?
Independent sample t-test is a statistical test used to compare the means of two independent groups. The groups are independent because the data in one group is not related to the data in the other group. For example, you might want to compare the average weight of male and female students in a class. In this case, male and female are two independent groups. Independent sample t-test is used to determine whether the difference in means of these two groups is statistically significant.
To conduct an independent sample t-test, you need to have two groups of data, a dependent variable, and an independent variable. The dependent variable is the one you are measuring, and the independent variable is the one that is used to classify the data into different groups.
Independent Sample T-Test Example Problems With Solutions Pdf
Here are some independent sample t-test example problems with solutions pdf:
Example 1:
Suppose you want to compare the average height of male and female students in a class. You take a random sample of 20 male students and 20 female students and measure their heights.
Male height data: 63, 65, 67, 68, 69, 70, 71, 71, 72, 72, 73, 73, 74, 75, 75, 76, 77, 78, 79, 80
Female height data: 58, 59, 60, 60, 61, 62, 63, 64, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75
Using independent sample t-test, you want to determine whether there is a significant difference in the average height of male and female students in the class.
Solution:
Step 1: Define the null and alternative hypotheses
The null hypothesis (H0): The average height of male and female students in the class is the same.
The alternative hypothesis (Ha): The average height of male and female students in the class is different.
Step 2: Set the significance level
Let's assume the significance level is 0.05.
Step 3: Compute the test statistic
The formula to calculate the independent sample t-test is:
Where:
t = test statistic
x̄1 = mean of group 1
x̄2 = mean of group 2
s1 = standard deviation of group 1
s2 = standard deviation of group 2
n1 = sample size of group 1
n2 = sample size of group 2
Using the data from our example:
x̄1 = 71.5 (mean of male group)
x̄2 = 65.5 (mean of female group)
s1 = 5.563 (standard deviation of male group)
s2 = 5.163 (standard deviation of female group)
n1 = 20 (sample size of male group)
n2 = 20 (sample size of female group)
Plugging these values into the formula:
The test statistic is equal to 4.2.
Step 4: Find the p-value
Using a t-table or statistical software, we can find that the p-value is less than 0.001.
Step 5: Compare the p-value with the significance level
The p-value is less than the significance level (0.05). Therefore, we reject the null hypothesis and conclude that there is a significant difference in the average height of male and female students in the class.
Example 2:
Suppose you want to compare the test scores of students who took a prep course and those who did not take a prep course. You take a random sample of 30 students who took a prep course and a random sample of 30 students who did not take a prep course.
Prep course student score data: 75, 80, 82, 85, 87, 88, 90, 90, 91, 92, 93, 93, 94, 95, 96, 96, 97, 98, 98, 99, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100
No prep course student score data: 60, 64, 65, 67, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96
Using independent sample t-test, you want to determine whether students who took a prep course have significantly higher test scores than those who did not take a prep course.
Solution:
Step 1: Define the null and alternative hypotheses
The null hypothesis (H0): There is no significant difference in the test scores of students who took a prep course and those who did not take a prep course.
The alternative hypothesis (Ha): Students who took a prep course have significantly higher test scores than those who did not take a prep course.
Step 2: Set the significance level
Let's assume the significance level is 0.05.
Step 3: Compute the test statistic
The formula to calculate the independent sample t-test is:
Where:
t = test statistic
x̄1 = mean of group 1
x̄2 = mean of group 2
s1 = standard deviation of group 1
s2 = standard deviation of group 2
n1 = sample size of group 1
n2 = sample size of group 2
Using the data from our example:
x̄1 = 95 (mean of prep course group)
x̄2 = 79.6 (mean of no prep course group)
s1 = 7.071 (standard deviation of prep course group)
s2 = 10.267 (standard deviation of no prep course group)
n1 = 30 (sample size of prep course group)
n2 = 30 (sample size of no prep course group)
Plugging these values into the formula:
The test statistic is equal to 5.35.
Step 4: Find the p-value
Using a t-table or statistical software, we can find that the p-value is less than 0.001.
Step 5: Compare the p-value with the significance level
The p-value is less than the significance level (0.05). Therefore, we reject the null hypothesis and conclude that students who took a prep course have significantly higher test scores than those who did not take a prep course.
Conclusion
Independent sample t-test is a statistical test used to compare the means of two independent groups. It is a powerful tool in statistics and can be used in many situations. In this article, we discussed independent sample t-test example problems with solutions pdf that will help you understand this statistical test better. By following the steps outlined in these examples, you can easily perform an independent sample t-test and draw meaningful conclusions from your data.