Understanding t-tests for independent and dependent samples

This article explains the concepts of t-tests for independent and dependent samples with examples. It covers the formulas used for calculating t-value, degrees of freedom, and critical value. The article also includes two problems with solutions to help readers understand the application of t-tests in real-life scenarios. The subject covered is statistics, and the course code is PSYC 2525.

In Class Assignment 3
PSYC 2525
1. Given the following, what should you conclude?
t(24) = 2.001 and tcritical = 1.94
Get rid of the null hypothesis and take the research hypothesis
2. What is another term that statisticians use when talking of dependent tests? Explain.
The term that is used is “paired-sample.” A paired sample is used when each subject is
tested twice and it results in paired observations. It also determines whether the difference
mean between both sets is equal to zero. It also is measured between both sets to determine
whether they are both equal.
3. Identify which of the following is the formulas are used for calculating a t value for an
independent samples and a dependent samples test?
Independent samples test Dependent samples test
Problems:
4. Dr. Rob has developed a new drug that he believes can cure Zombieism and stop the
Zombie apocalypse. To test his new drug he captures 30 Zombies and randomly separates
them into two groups. One group receives his new drug the other a placebo.
a. What type of t-test would you use to see if the new drug had a significant effect?
The independent samples t-test that compares the means of two groups
b. What are the statistical hypotheses for this hypothesis (He wants to see a reduction in
Zombieism)?
H0: (there is no significant difference in the means of the two groups)
H1: (there is significant difference in the means of two groups)
c. Given the following data compute the t-test.
Drug No Drug
Mean: 28 45

s2: 25 48
n: 15 15
s: 5 6.93
t-test statistics, ,

d. What are the degrees of freedom for problem 1?
Degrees of freedom, df = = 15 + 15 – 2 = 28
e. What is the critical value to test problem one’s hypothesis?
Critical value, = t (28), p < 0.05 = 2.0484
The critical values = (-2.0484, 2.0484)
f. What can you conclude about Dr. Rob’s drug to cure Zombieism?
Since test statistics, t = -7.7059 < -2.0484, the critical value, thus Reject Ho. Therefore,
there is sufficient evidence to conclude that there is significant difference in the means of
the two groups. Conclusively, Dr. Rob’s drug seems to be effective.
5. Penny, a third grade teacher, has just returned from a teaching conference where she
learned about a new teaching method that is predicted to increase retention of new
information dramatically. Penny decides to test to see if the new teaching method she
learned works. To test the new teaching method Penny teaches using the old method for a
week and then gives a test for retention and then teaches using the new method the
following week and gives a retention test. There are 10 students in her class. Penny is not
sure if the new method will help or hinder her students.
a. What type of t-test would you use to see if the new teaching style had a significant
effect?
We use the dependent-samples (paired-samples) t test, which is used to compare the same
sample tested under different conditions.
b. What are the statistical hypotheses for this hypothesis (He wants to see a teaching
style improves retention of new information)?
H0: (there is no significant difference between the mean of the old
method and the mean of new method)

H1: (the mean of the new method is higher than the mean of the old
method)
c. Given the following data compute the t-test.
Old Method New Method D D2
30 42 12 144
26 29 3 9
33 17 -16 256
31 26 -5 25
35 35 0 0
21 31 10 100
25 22 -3 9
37 40 3 9
16 18 2 4
24 27 3 9 .
∑X1 = 278 ∑X2 = 287 ∑D = 9 ∑D2 = 565
Mean of the difference score = = 0.9
Variance of the difference score =
Standard Deviation = √61.878 = 7.866
 = 1.144
d. What are the degrees of freedom for problem 2?
The degree of freedom, df = n -1 = 10 -1 = 9
e. What is the critical value to test problem ones hypothesis?
This is one tailed test, therefore the critical value, t (9), p = 0.05 = 1.833
f. What can you conclude about the effectiveness of Penny’s new style of teaching?
The test statistic, t = 1.144 < 1.833, the critical value, thus We do not reject Ho. There is
sufficient evidence to support that, on average, the new teaching style had no significant
effect on the retention of information with students.