Twenty (20) students randomly assigned to an experimental group are studying for a test while listening to classical music. Thirty (30) students randomly assigned to a control group are studying for the same test in complete silence. Both groups take the test after studying for two weeks, and their performance on the test is as follows:
Exp
40-38-21-42-48-42-44-48-57-42-32-32-38-40-34-65-37-67-48-39-45-28-57-58-43-42-51-52-30-29-
Cont
51-25-33-42-40-55-50-24-38-21-38-38-54-29-52-58-30-25-20-28-26-44-38-35-34-26-30-32-50-30-
In this problem, you will determine what the experimenter should conclude
Using the 5% level of significance (alpha):
a) Determine the null and research hypotheses;
b) Select the correct template (templates for the Single Sample t-test, the Independent Samples t-test, and the ANOVA are included in the tabs that follow this tab);
c) Complete each of the blank cells in the template selected
d) State your conclusion, making reference to the test statistic, the critical value, the effect size, and your hypotheses.
a) Ho: music mean = silence mean
Ha: music mean ≠ silence mean
Independent Samples t-test
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
I'll let you fill in the blank cells.
a) The null hypothesis (H0) is that there is no difference in test performance between the experimental group (students studying with classical music) and the control group (students studying in silence). The research hypothesis (Ha) is that there is a difference in test performance between the two groups.
b) Since we are comparing the test performance of two different groups, the appropriate template to use is the Independent Samples t-test.
c) The blank cells in the template can be completed as follows:
Independent Samples t-test Template:
Group 1: Experimental Group (students studying with classical music)
Group 2: Control Group (students studying in silence)
Sample Size (n1): 20
Sample Mean (x̄1): Mean of the test scores in the experimental group (calculated by taking the sum of all test scores in the experimental group and dividing by the sample size)
Sample Standard Deviation (s1): Standard deviation of the test scores in the experimental group (calculated using the formula for sample standard deviation)
Sample Size (n2): 30
Sample Mean (x̄2): Mean of the test scores in the control group (calculated by taking the sum of all test scores in the control group and dividing by the sample size)
Sample Standard Deviation (s2): Standard deviation of the test scores in the control group (calculated using the formula for sample standard deviation)
(Remember to use the unbiased estimator if necessary, dividing by n-1 instead of n for sample standard deviation when the sample is less than the population).
With this information, we can calculate the t-statistic and compare it to the critical value.
d) To state the conclusion, we compare the calculated t-statistic to the critical value at the 5% level of significance (alpha). If the calculated t-statistic is greater than the critical value (rejecting the null hypothesis), we can conclude that there is a significant difference in test performance between the two groups. The effect size can be calculated using Cohen's d or another appropriate measure. It provides an indication of the magnitude of the difference between the groups.