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 Cont
30 30
18 28
20 32
40 42
50 30
40 40
40 42
48 34
56 36
42 24
32 38
36 32
38 20
40 30
34 42
40 40
30 30
50 20
48 20
30 18
16
24
28
22
34
22
30
32
30
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 (round to two decimal places).
D) State your conclusion, making reference to the test statistic, the critical value, the effect size, and your hypotheses.
A) Null and research hypotheses:
The null hypothesis (H0) is that there is no significant difference between the mean test scores of the experimental group (students studying with classical music) and the control group (students studying in silence).
H0: μ_exp = μ_cont
The research hypothesis (Ha) is that there is a significant difference between the mean test scores of the two groups.
Ha: μ_exp ≠ μ_cont
B) Template selection:
Based on the information provided, the appropriate template to use is the Independent Samples t-test, as we are comparing the means of two independent groups (experimental and control) to determine if there is a significant difference.
C) Completing the template:
The template requires the following information:
- Sample size (n)
- Sample mean (x̄)
- Sample standard deviation (s)
- Degrees of freedom (df)
For the experimental group:
n_exp = 20
x̄_exp = average of the scores: (30+18+20+40+50+40+40+48+56+42+32+36+38+40+34+40+30+50+48+30)/20 = 38.5
s_exp = standard deviation of the scores: We can calculate this using the formula for sample standard deviation or input the scores into a statistical software/tool.
df_exp = n_exp - 1 = 20 - 1 = 19
Similarly, for the control group:
n_cont = 30
x̄_cont = average of the scores: (30+28+32+42+30+40+42+34+36+24+38+32+20+30+42+40+30+20+18)/30 = 32.4
s_cont = standard deviation of the scores: We can calculate this using the formula for sample standard deviation or input the scores into a statistical software/tool.
df_cont = n_cont - 1 = 30 - 1 = 29
D) State your conclusion:
To determine the conclusion, we need to perform the independent samples t-test using the template values.
The independent samples t-test compares the means of two groups and provides a test statistic, a p-value, and associated critical values. We compare the test statistic to the critical value to determine if the difference in means is statistically significant.
We use a significance level (alpha) of 0.05 (5%), which means that if the calculated p-value is less than 0.05, we reject the null hypothesis in favor of the alternative hypothesis.
After performing the independent samples t-test and obtaining the test statistic and p-value, we compare the p-value to our significance level.
If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference between the mean test scores of the experimental and control groups.
If the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that there is no significant difference between the mean test scores of the two groups.
Therefore, to state the conclusion, you would need to perform the t-test and obtain the test statistic, p-value, and degrees of freedom. After that, compare the p-value to the significance level (alpha) of 0.05 and make the conclusion based on whether the p-value is less than or greater than 0.05.
A) The null and research hypotheses:
Null Hypothesis (H0): There is no significant difference in test performance between the experimental group (studying while listening to classical music) and the control group (studying in complete silence).
Research Hypothesis (H1): There is a significant difference in test performance between the experimental group and the control group.
B) The appropriate template to use in this scenario is the Independent Samples t-test template.
C) Completing the template:
1. Mean of the experimental group (X1): Calculate the mean of the experimental group test scores: X1 = (30 + 18 + 20 + 40 + 50 + 40 + 40 + 48 + 56 + 42 + 32 + 36 + 38 + 40 + 34 + 40 + 30 + 50 + 48 + 30) / 20
2. Standard deviation of the experimental group (SD1): Calculate the standard deviation of the experimental group test scores: SD1 = Calculate the sample standard deviation of the experimental group test scores.
3. Sample size of the experimental group (n1): Since there are 20 students in the experimental group, n1 = 20
4. Mean of the control group (X2): Calculate the mean of the control group test scores: X2 = (30 + 28 + 32 + 42 + 30 + 40 + 42 + 34 + 36 + 24 + 38 + 32 + 20 + 30 + 42 + 40 + 30 + 20 + 20 + 18) / 30
5. Standard deviation of the control group (SD2): Calculate the standard deviation of the control group test scores: SD2 = Calculate the sample standard deviation of the control group test scores.
6. Sample size of the control group (n2): Since there are 30 students in the control group, n2 = 30
D) State the conclusion:
To determine the conclusion, we need to calculate the t-statistic, degrees of freedom, critical value, and p-value using the completed template. Then we can compare the t-statistic with the critical value and check if the p-value is less than the significance level (alpha = 0.05).
Once these values are calculated, we can make a conclusion and mention the test statistic, critical value, effect size, and hypotheses in the conclusion statement.